We provide mathematical reasoning practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on mathematical reasoning skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of mathematical reasoning Questions

Question No | Questions | Class |
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1 | Given the true statement: If a quadrilateral is a square, then it is a rectangle. It follows that, of the converse and the inverse of this true statement. A. Only the converse is true B. only the inverse is true c. Both are true D. Neither is true E. The inverse is true, but the converse is sometimes true |
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2 | Given ( P: 25 ) is a multiple of ( 5, q: 25 ) is a multiple of 8. Write the compound statement connecting these two statements with “and”, “or” in ( 60^{t h} ) cases. Check the validity of the statement. |
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3 | Which of the following statements are true and which are false? In each case give a valid reason for saying so (i) ( p: ) Each radius of a circle is a chord of the circle (ii) ( mathrm{q}: ) The centre of a circle bisects each chord of the circle (iii) ( r: ) Circle is a particular case of an ellipse (iv) ( s: ) If ( x ) and ( y ) are integers such that ( boldsymbol{x}>boldsymbol{y} ) then ( -boldsymbol{x}<-boldsymbol{y} ) ( (v) t: sqrt{11} ) is a rational number |
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4 | Write down the negations for the following: (a) If the diagonals of a parallelogram are perpendicular then it is a rhombus. (b) Kanchanganga is in India and Everest is in Nepal. (c) The Sun is a star or the Jupiter is a planet. |
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5 | Which of the following statements is the inverse of “If you do not understand geometry, then you do not know how to reason deductively.”? A. If you reason deductively, then you understand geometry. B. If you understand geometry, then you reason deductively. c. If the do not reason deductively, then you understand geometry. D. None of these |
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6 | Assertion STATEMENT-1: The minimum value of the intercepts cut on tangent by a tangent to the ellipse ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1 ) between the coordinate axes is ( a+b ) Reason STATEMENT-2: For each pair of two negative real numbers a and b, nequality ( frac{boldsymbol{a}+boldsymbol{b}}{mathbf{2}} geq-sqrt{boldsymbol{a} boldsymbol{b}} ) holds. |
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7 | State the following statement is True or False The truth value of “4 is even and 8 is odd” is True A. True B. False |
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8 | The contrapositive of “if ( x ) has courage then ( x ) will win”, is A. If ( x ) will in, then ( x ) has courage B. If ( x ) has no courage, then ( x ) will not win. c. If ( x ) will not win, then ( x ) has no courage D. If ( x ) will not win, then ( x ) has courage |
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9 | The negation of the statement:”If become a teacher, then I will open a school” is A. I will become a teacher and I will not open a school. B. Either I will not become a teacher or I will not open a school c. Neither I will become a teacher nor I will open a school D. I will not become a teacher or I will open a school. |
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10 | Negation of the statement ( p: ) for every real number, either ( x>1 ) or ( x<1 ) is | 11 |

11 | Check the validity of the following statement: ( boldsymbol{p}: 125 ) is a multiple of 5 and 7 A. True B. False |
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12 | Assertion ( (A): P(n)=n^{2}+n+41 ) is a prime ( forall boldsymbol{n} in boldsymbol{N} ) Reason (R): If a number is prime then it contains only two factors; 1 and number itself. A. Both (A) & (R) are individually true & (R) is correct explanation of (A). B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A) c. (A)is true but (R) is false. D. (A)is false but (R) is true |
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13 | “No square of a real number is less than zero” is equivalent to A. for every real number a, ( a^{2} ) is non negative. ( mathbf{B} cdot forall a in R, a^{2} geq 0 ) C . either (1) or (2). D. None of these |
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14 | The dual of the following statement “Reena is healthy and Meena is beautiful”‘ is A. Reena is not beaufiful and Meena is not healthy B. Reena is not beautiful or Meena is not healthy. c. Reena is not healthy or Meena is not beautiful. D. None of these. |
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15 | Find the quantifier which best describes the variable of the open sentence ( x^{2}+2 geq 0 ) A. Universal. B. Existential. c. Neither (a) nor (b) D. Does not exist. |
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16 | Which of the following sentences are NOT a statement? ( A cdot 9 ) is less than 7 B. The sun is a star. c. There is no rain without clouds D. Mathematics is fun. |
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17 | Write the converse, inverse and contrapositive of the following statements: “If a function is differentiable then it is continuous”. |
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18 | ( boldsymbol{p}: ) He is hard working. ( boldsymbol{q}: ) He will win The symbolic form of “If he will not win then he is not hard working”, is ( mathbf{A} cdot p Rightarrow q ) в. ( (sim p) Rightarrow(sim q) ) c. ( (sim q) Rightarrow(sim p) ) D. ( (sim q) Rightarrow p ) |
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19 | Show that the statement ( boldsymbol{p}: ) If ( boldsymbol{x} ) is a real number such hat ( boldsymbol{x}^{mathbf{3}}+ ) ( 4 x=0, ) then ( x ) is 0 is true by direct method |
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20 | Determine the contrapositve of each of the following statements: If he has courage he will win. |
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21 | The converse of “If ( x ) has courage, then ( x ) will win”, is A. If ( x ) wins, then ( x ) has courage. B. If ( x ) has no courage, then ( x ) will not win. C. If ( x ) will not win, then ( x ) has no courage. D. If ( x ) will not win, then ( x ) has courage. |
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22 | ( sim[(boldsymbol{p} wedge boldsymbol{q}) rightarrow(sim boldsymbol{p} vee boldsymbol{q})] ) is A. Tautology B. Contradiction c. Neither (A) nor (B) D. Either (A) or (B) |
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23 | If ( p, q, r ) have truth values ( T, F, T ) respectively, then which of the following is True? A ( cdot(p rightarrow q) wedge r ) в. ( (p rightarrow q) wedge sim r ) c. ( (p wedge q) wedge(p vee r) ) D. ( q rightarrow(p wedge r) ) |
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24 | Negation of “A is in Class ( X^{t h} ) or ( B ) is in ( boldsymbol{X} boldsymbol{I} boldsymbol{I}^{t h^{prime prime}} ) is A. A is not in class ( X^{t h} ) but ( B ) is in ( X I I^{t h}^{h} ) c. Either A is not in class ( X^{t h} ) or ( mathrm{B} ) is not in ( X I I^{t h} ) D. none of these |
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25 | Determine the contrapositive of the following statement: If ( x ) is an integer and ( x^{2} ) is odd, then ( x ) is odd. |
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26 | Given: All seniors are mature students. Which statement expresses a conclusion that logically follows from the given statement? A. All mature students are seniors B. If Bill is a mature student, then he is a senior C. If Bill is not a mature student, then he is not a senior D. If Bill is not a senior, then he is not a mature student E. All sophomores are not mature students. |
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27 | State whether the following statement is True or False. The sum of two odd numbers and one |
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28 | If ( boldsymbol{x}=mathbf{5} ) and ( boldsymbol{y}=-mathbf{2}, ) then ( boldsymbol{x}-mathbf{2} boldsymbol{y}=mathbf{9} ) The contrapositive of this statement is/are A. If ( x-2 y neq 9 ), then ( x neq 5 ) or ( y neq 2 ) B. If ( x-2 y neq 9 ), then ( x neq 5 ) and ( y neq-2 ) c. If ( x-2 y=9 ), then ( x=5 ) and ( y=-2 ) D. none of these. |
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29 | 71. The Boolean expression ~ (pvqvp^q) is equivalent to : (a) P (6) 9 (c) ~q [JEE M 2018] (d) ~P |
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30 | State whether the following statement is True or False. The product of two even numbers is always even. A. True B. False |
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31 | Prepare the truth table for the following. ( sim boldsymbol{p} wedge boldsymbol{q} ) |
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32 | Which of the following is a statement? ( A ). I am Lion. B. Logic is an interesting subject C. A triangle is a circle and 10 is a prime number D. None of these. |
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33 | The length ( L ) (in centimetre) of a copper rod is a linear function of its Celsius temperature ( C . ) In an experiment, if ( L=124.942 ) when ( C= ) 20 and ( L=125.134 ) when ( C=110 ) express ( L ) in terms of ( C ) |
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34 | State the following statement is True or False If Shelly does not like John, then the truth value of the statement “Shelly likes Mike and she likes John” is True A. True B. False |
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35 | Prove that ( 3+sqrt{7} ) is irrational number. | 11 |

36 | ( p: H e ) is hard working. ( boldsymbol{q}: ) He is intelligent. Then ( sim boldsymbol{q} Rightarrow sim boldsymbol{p}, ) represents A. If he is hard working, then he is not intelligent. B. If he is not hard working, then he is intelligent c. If he is not intelligent, then he is not had working D. If he is not intelligent, then he is hard working |
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37 | Contrapositive of the statement ‘If two number are not equal, then their squares are not equal’, is: |
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38 | Write the negation of the following statements: (i) Chennai is the capital of Tamil Nadu (ii) ( sqrt{2} ) is not a complex number (iii) All triangles are not equilateral triangle (iv) The number 2 is greater than 7 (v) Every natural number is an integer |
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39 | Find the total surface area of a closed cylindrical petrol storage tank whose diameter ( 4.2 mathrm{m} ) and height ( 4.5 mathrm{m} ) |
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40 | Write the negation of the following statements i) ( sqrt{7} ) is a rational number. ii) Length of both diagonals of any rectangle are equal |
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41 | The converse of ( boldsymbol{p} Rightarrow boldsymbol{q} ) is ( mathbf{A} cdot p Rightarrow q ) в. ( q Rightarrow p ) c. ( -p Rightarrow-q ) ( mathbf{D} cdot-q Rightarrow-p ) |
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42 | The negation of the statement “2 ( +3= ) ( 5^{prime prime} ) and ” ( 810 ) c. ( 2+3 neq 5 ) or ( 8 nsupseteq 10 ) D. None of these |
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43 | Consider the statement, Given that people who are in need of refuge and consolation are apt to do odd things, it is clear that people who are apt to do odd things are in need of refuge and consolation. This statement, of the form ( (P Rightarrow Q) Rightarrow(Q Rightarrow P), ) is logically equivalent to A. People who are in need of refuge and consolation are not apt to do odd things. B. People are apt to do odd things if and only if they are in need of refuge and consolation. C. People who are apt to do odd things are in need of refuge and consolation. D. People who are in need of refuge and consolation are apt to do odd things |
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44 | Negation of the statement “Every natural number is an integer”” A. All natural numbers are whole numbers. B. Every natural number is not an integer. c. Every natural number is not a real number. D. none of the above |
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45 | The statement form ( (boldsymbol{p} Leftrightarrow boldsymbol{r}) Rightarrow(boldsymbol{q} Leftrightarrow boldsymbol{r}) ) is equivalent to ( mathbf{A} cdot[(sim p vee r) wedge(p vee sim r)] vee sim[(sim q vee r) wedge(q vee sim r)] ) ( mathbf{B} cdot sim[(sim p vee r) wedge(p vee sim r)] wedge[(sim q vee r) vee(q vee sim r)] ) ( mathbf{c} cdot[(sim p vee r) wedge(sim p vee sim r)] wedge[(sim q vee r) wedge(q vee sim r)] ) ( mathbf{D} cdot sim[(sim p vee r) wedge(p vee sim r)] wedge[(sim q vee r) wedge(q vee sim r)] ) |
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46 | The compound statement, “If you won the race; then you did not run faster than others” is equivalent to A. “If you won the race, then you ran faster than others”” B. “If you ran faster than others, then you won the race”” C. “If you did not win the race, then you did not run faster than others”” D. “If you ran faster than others, then you did not win the race” |
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47 | when does the current flow from A to B? A. p is open, q is open, ris closed B. p is closed, q is open, ris closed c. p is closed, q is closed, ris open D. p is open, q is closed, ris closed |
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48 | Determine the contrapositve of each of the following statements:
It is necessary to be strong in order to be a sailor. |
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49 | State whether the following statement is True or False. The sum of three odd numbers is even. |
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50 | Inverse of a statement can be explained as A. Negating both the hypothesis and conclusion of a conditional statement B. Antecedent is the negation of the original antecedent and whose consequent is the negation of the original consequent. c. both are correct D. none is correct |
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51 | The negative of the statement “lf a number is divisible by 15 then it is divisible by 5 or ( 3 ” ) A. if a number is divisible by 15 then it is not divisible by and 3 B. a number is divisible by 15 and it is not divisible by 5 o 3 c. a number is divisible by 15 or it is not divisible by 5 and 3 D. a number is divisible by 15 and it is not divisible by 5 and 3 |
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52 | What is true about the statement “If two angles are right angles the angles have equal measure” and its converse “If two angles have equal measure then the two angles are right angles”? A. The statement is true but its converse is false B. The statement is false but its converse is true c. Both the statement and its converse are false D. Both the statement and its converse are true |
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53 | In the above network, current flows from ( T ) to ( M, ) when A. p closed, q closed and ropened B. p closed, q opened and r closed c. p opened; q closed and r closed D. All the above |
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54 | The negative of the statement “If a number is divisible by 15 then it is divisible by 5 or ( 3^{prime prime} ) A. If a number is not divisible by ( 15, ) then it is not divisible by 5 and 3 B. A number is divisible by 15 and it is not divisible by 5 or 3 C. A number is not divisible by 15 or it is not divisible by 5 and 3 D. A number is divisible by 15 and it is not divisible by 5 and 3 |
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55 | Check the validity of the following statement: ( boldsymbol{p}: mathbf{1 0 0} ) is a multiple of ( mathbf{4} ) and ( mathbf{5} ) A. True B. False |
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56 | Write the component statement of the following compounds statements and check whether the compound statement is true or false: All rational number are real and all real number are not complex. |
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57 | 66. The Boolean Expression (pAqvqVP9 equivalent to: JEE M 2016] (a) pUq (b) PV~9 (c) ~paq (d) pUq |
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58 | “If ( p, ) then ( q^{prime prime} ) is logically equivalent to which of the following? I. If ( q, ) then ( p ) II. If not ( p, ) then not ( q ) III. If not ( q, ) then not ( p ) A. None of the above B. III Only c. I and II only D. I and III only E. I, II and III |
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59 | Negate each of the following statements: There exists a number which is equal to ¡ts square. |
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60 | Tell whether the following is certain to happen, impossible can happen but not certain. A tossed coin will land heads up. |
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61 | Which of the following connectives satisfy commutative law? ( A cdot wedge ) B. ( c cdot Leftrightarrow ) D. All the above |
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62 | Write converse of statement. In ( Delta A B C ) if ( A B=A C ) then ( C=B ) |
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63 | When electric current is passed through acidified water for 1930 s, ( 1120 mathrm{mL} ), of ( H_{2} ) gas is collected (at STP) at the cathode. What is the current passed in amperes? A . 0.05 B. 0.50 ( c . ) 5. D. 50 |
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64 | The inverse of the statement “lf a number is divisible by 4 then it is also divisible by ( 2^{prime prime} ) is – A. If a number is divisible by 4 , then it is always divisible by 2 B. If a number is not divisible by 4 , then it is divisible by 2. c. If a number is not divisible by ( 4, ) then it is not divisible by 2. D. None of the above |
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65 | Assertion Triangles on the same base and between the same parallel lines are equal in area. Reason The distance between two parallel lines is same everywhere. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct |
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66 | Tell if the following statement is true or false. In case give a valid reason for saying so ( boldsymbol{p}: ) Each radius of a circle is a chord of the circle. A. True B. False |
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67 | Which of the following statements is the inverse of “lf you do not understand geometry, then you do not know how to reason deductively.” ? A. If you reason deductively, then you understand geometry. B. If you understand geometry, then you reason deductively c. If the do not reason deductively, then you understand geometry D. None of the above |
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68 | In which of the following cases, ( boldsymbol{p} Leftrightarrow boldsymbol{q} ) is true? A . p is true, q is true B. p is false, q is true c. p is true, q is false. D. None of these. |
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69 | the following (a) 20.0 (U 101 47. Let S be a non-empty subset of R. Consider the follow statement : P: There is a rational number x € S such that x>0. Which of the following statements is the negation of the statement P? [2010] (a) There is no rational number x e S such than x<0. (b) Every rational number x ES satisfies x<0. (C) XE S and x<0 = x is not rational. (d) There is a rational number x e S such that x<0. following relations: |
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70 | In the above network, current flows from ( M ) to ( N, ) when A. ( q ) closed, ropened and p closed B. q opened, p opened and r closed. C. q opened, p closed and r closed. D. q closed, p closed and r opened |
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71 | If ( P(n) ) be the statement ( n(n+1), n in ) ( N ) is even, then A ( . P(2) ) is true B. ( P(3) ) is true c. ( P(4) ) is true D. all of the above |
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72 | ( boldsymbol{p} leftrightarrow boldsymbol{q} ) is equivalent to ( mathbf{A} cdot p rightarrow q ) ( mathbf{B} cdot q rightarrow p ) ( mathbf{c} cdot(p rightarrow q) vee(q rightarrow p) ) D. ( (p rightarrow q) wedge(q rightarrow p) ) |
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73 | If ( P(n) ) be the statement ( n(n+1)+1 ) is odd, then which of the following is false? A ( . P(2) ) в. ( P(3) ) c. ( P(4) ) D. none of these |
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74 | Which of the following statements is the inverse of “Our pond floods whenever there is a |
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75 | Determine the contrapositive of the following statement: It never rains when it is cold. |
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76 | the negation of M 2019-9 April 76. For any two statements p and q, the ne expression p v (p^q) is: [JEEM 2019_ (a) ~pa-q (b) paq (c) pHq (d) “p V-9 |
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77 | State whether the following sentence is always true, always false or ambiguous. Justify your answer February has only 28 days. | 11 |

78 | State whether the statement ( p: ) If ( x ) is a real number such that ( x^{3}+ ) ( 19 x=0, ) then ( x ) is 0 is true / False A. True B. False |
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79 | State whether the following sentence is always true, always false or ambiguous. Justify your answer. Makarasankranthi falls on a Friday. | 11 |

80 | Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident. A. If you lose the game then you dont know the rules or you are overconfident B. A sufficient condition that you win the game is that you know the rules or you are not overconfident c. If you dont know the rules or are overconfident you lose the game D. If you know the rules and are overconfident then you win the game |
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81 | The contrapositive of ( sim boldsymbol{p} rightarrow(boldsymbol{q} rightarrow sim boldsymbol{r}) ) is ( mathbf{A} cdot(q wedge r) rightarrow p ) в. ( (q rightarrow r) rightarrow p ) c. ( (q vee r) rightarrow p ) D. None of these. |
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82 | The converse of “If in a triangle ( A B C, A B=A C, ) then ( angle B=angle C^{prime prime}, ) is A. If in a triangle ( A B C, angle B=angle C ), then ( A B=A C ). B. If in a triangle ( A B C, A B neq A C ), then ( angle B neq angle C ). c. If in a triangle ( A B C, angle B neq angle C ), then ( A B neq A C ). D. If in a triangle ( A B C, angle B neq angle C ), then ( A B=A C ). |
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83 | Which of the following is always true? ( mathbf{A} cdot sim(p rightarrow q) equiv sim p wedge q ) В . ( (p vee q) equiv sim p vee sim q ) c. ( sim(p Rightarrow q) equiv(p wedge sim q) ) D. ( (p wedge q) equiv sim p wedge sim q ) |
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84 | is an irrational number”, q be the dental number”, and r be the [2008] U=1, D-6 (d) a= 3, D = 4 Let p be the statement is an irrational number 19 statement “y is a transcendental number”, and statement “x is a rational number iffy is a transcende number”. Statement-1 :ris equivalent to either q or p Statement-2:ris equivalent to (p4-9). (a) Statement -1 is false, Statement-2 is true (b) Statement-1 is true, Statement-2 is true; Statement- a correct explanation for Statement-1 (C) Statement -1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1 (d) Statement -1 is true, Statement-2 is false The statom 42. |
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85 | The negation of ( sim s vee(sim r wedge s) ) is equivalent to ( mathbf{A} cdot S wedge r ) В. ( S wedge sim(r wedge sim s) ) c. ( S vee sim(r wedge sim s) ) D. None of These |
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86 | Show that the following statement is true by the method of contrapositive ( p: ) If ( x ) is an integer and ( x^{2} ) is even then ( x ) is also even |
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87 | The negation of ( boldsymbol{q} vee sim(boldsymbol{p} wedge boldsymbol{r}) ) is? | 11 |

88 | 69. The following statement (p →q) → [(p ) →q] is : (a) a fallacy (b) a tautology (c) equivalent to – p > (d) equivalent to p–9 [JEEM 2017] |
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89 | The inverse of statement is ” If you grew in Alaska, then you have seen snow.” A. “If you did not grow up in Alaska, then you have not seen snow.” B. “If you grow up in Alaska, then you have not seen snow.” C. “If you did not grow up in Alaska, then you have seen snow.” D. None of these |
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90 | “If we control population growth, then we prosper”. Negative of this proposition is: A. If we do not control population growth, we prosper B. If we control population, we do not prosper c. we control population and we do not prosper D. If we don’t control population, we do not prosper |
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91 | ( sim(boldsymbol{p} wedge boldsymbol{q}) equiv ) ( mathbf{A} cdot sim p vee sim q ) в. ( p vee sim q ) ( mathrm{c} cdot sim p vee q ) D. None |
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92 | Determine whether the following compound statement are true of false: Delhi is in England and ( 2+2=4 ) A . True B. False |
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93 | When does the truth value of the statement ( (boldsymbol{p} vee boldsymbol{r}) Leftrightarrow(boldsymbol{q} vee boldsymbol{r}) ) become true? A . p is true, q is true B. p is false, q is false c. p is true, r is true D. Both (1) and (3) |
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94 | Let ( p: A ) triangle is equilateral, ( q: A ) triangle is equiangular then inverse of ( boldsymbol{q} rightarrow boldsymbol{p} ) is A. If a triangle is not equilateral then it is not equiangular B. If a triangle is not equiangular then it is not equilateral C. If a triangle is equiangular then it is not equilateral D. If a triangle is equiangular then it is equilateral |
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95 | Determine the contrapositve of each of the following statements: If ( x ) is less than zero, then ( x ) is not positive. |
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96 | ( sim(p Leftrightarrow q) ) is equivalent to ( mathbf{A} cdot sim p wedge sim q ) B ( . sim p vee sim q ) ( mathbf{C} cdot(p wedge sim q) vee(sim p wedge q) ) D. none of these |
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97 | ( boldsymbol{p}: ) He is hard working. ( boldsymbol{q}: ) He will win The symbolic form of “He is hard working then he will win”, is A ( . p vee q ) в. ( p wedge q ) ( mathbf{c} cdot p Rightarrow q ) D. ( q Rightarrow p ) |
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98 | State whether true or false. The sum of the interior angles of a quadrilateral is ( 350^{circ} ) A. True B. False |
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99 | Consider the following three statements: ( P: 5 ) is a prime number ( Q: 7 ) is a factor of 192 ( mathrm{R}: ) L.C.M. of 5 and 7 is 35 Then the truth value of which one of thefollowing statements is true? A ( cdot(P wedge Q) vee(sim R) ) в. ( (sim P) wedge(sim Q wedge R) ) c. ( (sim P) vee(Q wedge R) ) D. ( P vee(sim Q wedge R) ) |
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100 | Given the following six statements: (1) All women are good drivers (2) Some women are good drivers (3) No men are good drivers (4) All men are bad drivers (5) At least one man is a bad driver (6) All men are good drivers. The statement that negates statement (6) is: A . (1) B. (2) ( c cdot(3) ) ( D cdot(4) ) E. (5) |
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101 | The contrapositive statement of statement “If ( x ) is prime number, then ( x ) is odd” is A. If ( x ) is not is prime number, then ( x ) is not odd B. If ( x ) is not odd, then ( x ) is not a prime number c. If ( x ) is a prime number, then ( x ) is not odd D. If ( x ) is not a prime number, then ( x ) is odd |
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102 | 42. [2008] (d) Statement -I is true, Statement-2 15 ans The statement p → (qp) is equivalent to (a) p (p9) (b) p (pvq) (c) p (p ) (d) p (p ) |
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103 | Find the component statements of the following compound statements and check whether they are true or false (i) Number 3 is prime or it is odd (ii) All integers are positive or negative (iii)100 is divisible by 3,11 and 5 |
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104 | The Boolean expression ( ((boldsymbol{p} wedge boldsymbol{q}) vee ) ( (p vee sim q)) wedge(sim p wedge sim q) ) is equivalent to : ( mathbf{A} cdot p wedge(sim q) ) B . ( p vee(sim q) ) c. ( (sim p) wedge(sim q) ) D. ( p wedge q ) |
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105 | “If Deb and Sam go to the mall then it is snowing” Which statement below is logically equivalent? A. If Deb and Sam do not go to the mall then it is not snowing B. If Deb and Sam do not go to the mall them it is snowing C. If it is snowing then Deb and Sam go to the mall D. If it is not snowing then Deb and Sam do not go to the mal |
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106 | Consider the statement, if ( n ) is divisible by 30 then ( n ) is divisible by 2,3 and by 5 Which of the following statements is equivalent to this statement?? A. If ( n ) is not divisible by 30 then ( n ) is divisible by 2 or divisible by 3 or divisible by 5 B. If ( n ) is not divisible by 30 then ( n ) is not divisible by 2 or not divisible by 3 or not divisible by 5 c. If ( n ) is divisible by 2 and divisible by 3 and divisible by 5 then ( n ) is divisible by 30 D. If ( n ) is not divisible by 2 or not divisible by 3 or not divisible by 5 then ( n ) is not divisible by 30 |
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107 | The contrapositive of ( (boldsymbol{p} vee boldsymbol{q}) Rightarrow boldsymbol{r} ) is A ( cdot r Rightarrow(p vee q) ) в. ( r Rightarrow(p vee q) ) c. ( r Rightarrow sim p wedge sim q ) D. ( R Rightarrow(q vee r) ) |
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108 | State true or false. A rhombus is a parallelogram. A. True B. False |
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109 | If ( boldsymbol{x}=mathbf{5} ) and ( boldsymbol{y}=mathbf{2} ) then ( boldsymbol{x}-mathbf{2} boldsymbol{y}=mathbf{9 . T h e} ) contrapositive of this statement is A. If ( x-2 y neq 9 ) then ( x neq 5 ) or ( y neq 2 ) B. If ( x-2 y neq 9 ) then ( x neq 5 ) and ( y neq-2 ) c. If ( x-2 y=9 ) then ( x=5 ) and ( y=-2 ) D. none of these. |
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110 | Which of the following statements is the converse of “If the moon is full, then the vampires are prowling.”? A. If the vampires are prowling, then the moon is full. B. If the moon is not full, then the vampires are prowling C. If the vampires are not prowling, then the moon is not full D. None of these |
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111 | Here are some words translated from an artificial language mie pie is blue light mie tie is blue berry aie tie is raspberry Which words could possibly mean “light fly”? A. pie zie B. pie mie c. aie zie D. aie mie |
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112 | The negation of the statement, “l go to school everyday”, is A. I never go to school. B. Some days, I do not go to school. c. Not all the days I do not go to school. D. All days I go to school. |
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113 | The converse of ( boldsymbol{p} Rightarrow boldsymbol{q}, ) is ( mathbf{A} cdot p Rightarrow q ) в. ( q Rightarrow p ) c. ( sim p Rightarrow sim q ) D. ( q Rightarrow sim p ) |
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114 | The converse of: “If two triangles are congruent then they are similar” is A. If two triangles are similar then they are congruent. B. If two triangles are not congruent then they are not similar. C. If two triangles are not similar then they are not congruent D. None |
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115 | The inverse of: “If two triangle are congruent then they are similar” is A. If two triangles are similar then they are congruent. B. If two triangles are not congruent then they are not ( operatorname{similar} ) c. If two triangles are not similar then they are not congruent. D. None |
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116 | Write the negations of the following statements: (a) All students of this college live in the hostel. (b) 6 is an even number or 36 is a perfect square |
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117 | Write opposite of the following: a)30 ( k m ) north b)Increase in weight c) Loss of ( R s .700 ) d) ( 100 m ) above sea level |
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118 | Find the inverse of the statement,” If ( triangle A B C ) is equilateral, then it is isosceles”. ( mathbf{A} cdot ) If ( triangle A B C ) is isosceles, then it is equilateral B. If ( triangle A B C ) is not equilateral, then it is isosceles. C. If ( triangle A B C ) is not equilateral, then it is not isosceles. D. If ( triangle A B C ) is not isosceles, then it is not equilateral. |
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119 | The converse of “if in a triangle ( A B C, A B>A C, ) then ( angle C=angle B^{prime prime}, ) is ( mathbf{A} cdot ) If in a triangle ( A B C, angle C=angle B, ) then ( A B>A C ) B. If in a triangle ( A B C, A B not=A C, ) then ( angle C not=angle B ). C. If in a triangle ( A B C, angle C not=angle B, ) then ( A B not=A C ) D. If in a triangle ( A B C, angle C not=angle B, ) then ( A B>A C ). |
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120 | Consider statement “If I do not work, I will sleep. If I am worried, I will not sleep. Therefore if I am worried, I will work”. This statement is A. valid B. invalid c. a fallacy D. none of these |
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121 | The inverse of statement” If a quadrilateral is a rectangle,then it has two pairs of parallel sides.” A. If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides. B. If a quadrilateral is a rectangle, then it has two pairs of parallel sides. C. If a quadrilateral does not have two pairs of parallel sides, then it is not a rectangle. D. None of these |
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122 | Are the following pairs of statements negations of each other? (i) The number ( x ) is not a rational number The number ( x ) is not an irrational |
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123 | The contrapositive of ( boldsymbol{p} rightarrow(sim boldsymbol{q} rightarrow sim boldsymbol{r}) ) is A ( cdot(sim q wedge r) rightarrow sim p ) в. ( (q rightarrow r) rightarrow sim p ) c. ( (q vee sim r) rightarrow sim p ) D. none of these. |
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124 | ( sim(p vee q) vee(sim p wedge q) ) is logically equivalent to ( mathbf{A} cdot sim p ) B. ( c cdot q ) ( mathrm{D} cdot sim q ) |
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125 | If ( p ) and ( q ) are two statement then ( (p leftrightarrow ) ( sim q) ) is true when A. ( p ) and ( q ) both are true B. ( p ) and ( q ) both are false C. ( p ) is false and ( q ) is true D. None of these |
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126 | ( (p wedge sim q) wedge(sim p wedge q) ) is a: A. A tautology B. A contradiction C. Both a tautology and a contradiction D. Neither a tautology nor a contradiction |
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127 | Determine the contrapositive of the following statements: If it snows, then they do not drive the car. |
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128 | The negation of ( boldsymbol{q} vee sim(boldsymbol{p} wedge boldsymbol{r}) ) is? ( mathbf{A} cdot sim q wedge sim(p vee r) ) В ( . sim q wedge(p wedge r) ) ( mathbf{c} cdot sim q vee(p wedge r) ) D. ( r vee(p wedge r) ) |
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129 | Write the component statement of the following compounds statements and check whether the compound statement is true or false: The sand heats up quickly in the sun and does not cool down fast at night |
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130 | If a sentence can be judged to be true or false, but not both then it is called A. an open sentence B. a statement c. a tautology. D. a contradiction. |
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131 | Find the truth value of 14 is a composite number or 15 is a prime no. |
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132 | ( (sim p wedge q) wedge q ) is A. a tautology B. a contradiction C. neither a tautology nor a contradiction D. none of these |
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133 | When ( y=3 ) which of the following is FALSE? A. ( y ) is prime and ( y ) is odd B. ( y ) is odd or ( y ) is even c. ( y ) is not prime and ( y ) is odd D. ( y ) is odd and ( 2 y ) is even |
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134 | Which of the following is not a statement? A. Every set is a finite set. B. Every square is a rectangle. c. The sun is a star. D. Shut the window. |
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135 | The converse of “if ( boldsymbol{x} in boldsymbol{A} cap boldsymbol{B} ) then ( boldsymbol{x} in ) ( A ) and ( x in B ” ), is A. If ( x in A ) and ( x in B ), then ( x in A cap B ) B. If ( x notin A cap B ), then ( x notin A ) or ( x notin B ). c. If ( x notin A ) or ( x notin B, ) then ( x notin A cap B ) D. If ( x notin A ) or ( x notin B ), then ( x in A cap B ). |
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136 | The inverse of “If two angles are congruent, then they have the same measure” is A. If two angles have the same measure, then they are congruent B. If two angles are not congruent, then they do not have the same measure C. If two angles do not have the same measure, then they are not congruent D. None of these |
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137 | Let ( boldsymbol{p}: mathbf{5 7} ) is an odd prime number ( q: 4 ) is a divisor of 12 ( boldsymbol{r}: mathbf{1 5} ) is the LCM of ( boldsymbol{3} ) and ( mathbf{5} ) be three simple logical statements. Which one of the following is true? A ( . p vee(sim q wedge r) ) В ( . sim p vee(q wedge r) ) c. ( (p wedge q) vee sim r ) D. ( (p vee(q wedge r) ) E . ( (p vee q) wedge r ) |
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138 | Determine the contrapositive of the following statement:
Only if he does not tire will he win. |
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139 | Assertion STATEMENT ( 1: sim(p leftrightarrow sim q) ) is equivalent to ( (boldsymbol{p} vee sim boldsymbol{q}) wedge(sim boldsymbol{p} vee boldsymbol{q}) ) Reason STATEMENT ( 2: sim(p leftrightarrow q) ) is equivalent to ( (boldsymbol{p} wedge sim boldsymbol{q}) vee(sim boldsymbol{p} wedge boldsymbol{q}) ) A. Statement 1 is True, Statement 2 is True; Statement 2 i a correct explanation for Statement 1 B. Statement 1 is True, Statement 2 is True ; Statement 2 is NOT a correct explanation for Statement 1 c. statement 1 is True, Statement 2 is False D. Statement 1 is False, Statement 2 is True |
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140 | Find truth value of compound statement ‘All natural number are even or odd” |
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141 | The converse of the contrapositive of the conditional ( boldsymbol{p} rightarrow sim boldsymbol{q} ) is : A ( . p rightarrow q ) в. ( p rightarrow sim q ) ( mathbf{c} . sim q rightarrow p ) ( mathbf{D} cdot sim p rightarrow q ) |
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142 | Which of the following statements is the inverse of “Our pond floods whenever there is a thunderstorm.”? A. If there is a thunderstorm, then our pond floods B. If we do not get a thunderstorm, then our pond does not flood. c. If our pond does not flood, then we did not get a thunderstorm D. None of these |
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143 | Negation of ” ( 2+3=5 ) and ( 8<10 " ) is A ( .2+3 neq 5 ) and ( <10 ) B. ( 2+3=5 ) and ( 8 Varangle 10 ) ( c cdot 2+3 neq 5 ) or ( 8 Varangle 10 ) D. None of the above |
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144 | The cost of an article including the sales tax is ( R s .616 . ) The rate of sales ( operatorname{tax} ) is ( 10 %, ) if the shopkeeper has made a profit of ( 12 %, ) then the cost price of the article is? A. Rs .350 в. ( R s .400 ) c. ( R s .500 ) D. Rs .800 |
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145 | The contrapositive of the statement ‘If am not feeling well, then I will go to the doctor’ is: A. If I am feeling well, then I will not go to the doctor B. If / will go to the doctor, then I am felling well c. If 1 will not go to the doctor, then I am feeling well D. If I will go to the doctor, then I am not feeling well |
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146 | The converse of the statement “if ( boldsymbol{p}<boldsymbol{q} ) then ( p-x<q-x^{prime prime} ) is : A. If ( p q-x ) |
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147 | The negation of the compound proposition ( boldsymbol{p} vee(sim boldsymbol{p} vee boldsymbol{q}) ) is A ( . p wedge q ) B. ( c cdot f ) D. ( (p wedge q) wedge sim p ) |
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148 | State whether the following statement is True or False. Sum of two prime numbers is always |
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149 | The converse of ( boldsymbol{p} rightarrow(boldsymbol{q} rightarrow boldsymbol{r}) ) is ( mathbf{A} cdot(q wedge sim r) vee p ) в. ( (sim q vee r) vee p ) ( c cdot(q wedge sim r) wedge sim p ) ( p ) D. ( (q wedge sim r) wedge p ) |
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150 | The converse of the contrapositive of the conditional ( boldsymbol{p} rightarrow sim boldsymbol{q} ) is. A ( . p rightarrow q ) в. ( p rightarrow sim q ) ( mathbf{c} . sim q rightarrow p ) ( mathbf{D} cdot sim p rightarrow q ) |
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151 | Assertion Two distinct lines cannot have more than one point in common. Reason Any number of lines can be drawn through one point. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct |
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152 | State whether the following statement is True or False. Prime numbers do not have any factors. |
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153 | (d) 2 53. The negation of the statement [2012] “If I become a teacher, then I will open a school”, is : I will become a teacher and I will not open a school. (b) Either I will not become a teacher or I will not open a school. (c) Neither I will become a teacher nor I will open a school. (d) I will not become a teacher or I will open a school. BA Letr ben obseruation |
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154 | If a compound statement is made up of three simple statements, then the number of rows in the truth table is ( mathbf{A} cdot mathbf{8} ) B. 6 ( c cdot 4 ) D. |
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155 | Negation of “A is in Class ( X^{t h} ) or ( mathrm{B} ) is in ( X I I^{t h prime prime} ) is A. A is not in class ( X^{t h} ) but ( B ) is in ( X I I^{t h}^{h} ) C. Either A is not in class ( X^{t h} ) or ( B ) is not in ( X I I^{t^{t}} ) D. None of these. |
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156 | ( sim[boldsymbol{p} wedge(sim boldsymbol{q})]= ) ( mathbf{A} cdot sim p wedge sim q ) в. ( sim p vee sim q ) ( mathbf{c} . sim p wedge q ) ( mathrm{D} cdot sim p vee q ) |
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157 | Which of the following is a statement? ( A ). I am Lion. B. Logic is an interesting subject C. A triangle is a circle and 10 is a prime number D. None of these. |
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158 | If a compound statement is made up of three simple statements, then the number of rows in the truth table is |
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159 | Write the following statement in five different ways conveying the same meaning ( mathbf{p}: ) If triangle is equiangular then it is an obtuse angled triangle |
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160 | Identify the quantifier in the following statements and write the negation of the statements (i) There exists a number which is equal to its square (ii) For every real number ( x, x ) is less ( operatorname{than} x+1 ) (iii) There exists a capital for every state in India |
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161 | State whether the following statement is True or False.
The product of three odd numbers is odd. |
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162 | State the following statement is True or False f ( p, q, r ) are statements, with truth values ( mathrm{T} ), ( mathrm{F} ), ( mathrm{T} ) respectively, then the truth value of ( (sim p vee q) wedge sim r Rightarrow p ) is ( T ) A. True B. False |
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163 | Determine whether the argument used to check the validity of the following statement is correct. ( p: ) If ( x^{2} ) is irrational, then ( x ) is rational The statement is true because the number ( x^{2}=pi^{2} ) is irrational, therefore ( x=pi ) irrational. A. True B. False |
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164 | Which statement represents the inverse of the statement “If it is snowing then Skeeter wears a sweater”? A. If Skeeter wears a sweater then it is snowing B. If Skeeter does not wear a sweater then it is not snowing C. If it is not snowing then Skeeter does not wear a sweater D. If it is not snowing then Skeeter wears a sweater |
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165 | The converse of converse of the statement ( boldsymbol{p} Longrightarrow sim boldsymbol{q} ) is ( mathbf{A} cdot sim q Longrightarrow p ) в. ( p Longrightarrow q ) ( mathbf{c} cdot p Longrightarrow sim q ) D. ( q Longrightarrow sim p ) |
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166 | Earth is a planet. Choose the option that is a negation of this statement. A. Earth is round B. Earth is not round c. Earth revolves round the sun D. Earth is not a planet |
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167 | Write the truth values of following statements (i) 9 is a perfect square but 11 is a prime number. (ii) Moscow is in Russia. (iii) London is in France. |
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168 | when ( boldsymbol{x} in boldsymbol{R} ) Are the following pairs of the statements are negative of each other: The number ( x ) is a rational number. The number ( x ) is not an irrational number. If Yes put 1 else 0. |
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169 | STATEMENT: All cabbages are red. Which of the following statements shows that the statement above is FALSE? A. David is eating a red apple B. Bill is eating a green apple c. Alice is not eating a red cabbage D. Ted is eating a red cabbage E. Keisha is eating green cabbage |
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170 | Find the converse of the statement,”If ABCD is square, then it is a rectangle”. ( A . ) If ( A B C D ) is a square, then it is .not a rectangle. B. If ( A B C D ) is not a square, then i is a rectangle. C. if ABCD is a rectangle, then it is square. D. If ( A B C D ) is not a square, then it is not a rectangle. |
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171 | The contrapositive of ( (sim p wedge q) rightarrow sim r ) is equivalent to A. ( (p wedge q) rightarrow r ) в. ( (p wedge q) vee r ) c. ( r rightarrow(p vee sim q) ) D. none of these |
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172 | The inverse of “If ( x ) has courage, then ( x ) will win”, is ( mathbf{A} cdot ) If ( x ) will win, then ( x ) has courage. B. If ( x ) has no courage, then ( x ) will not win. C. If ( x ) will not win, then ( x ) has no courage. D. If ( x ) will not win, then ( x ) has courage. |
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173 | The negation of the statement ( boldsymbol{q} vee ) ( (p wedge sim r) ) is equivalent to ( mathbf{A} cdot sim q wedge(p rightarrow r) ) в. ( q vee sim(p rightarrow r) ) c ( cdot q wedge(sim p wedge r) ) D. None of these. |
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174 | 43. [2009] Statement-1: -(pH-q) is equivalent Statement-2 : – ( – 9) is a tautology (a) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statens (6) Statement-1 is true, Statement-2 is false. (c) Statement-1 is false, Statement-2 is true. (d) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement- on for Statement-1. |
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175 | The statement pattern ( (boldsymbol{p} wedge boldsymbol{q}) wedge[sim boldsymbol{r} vee ) ( (p wedge q)] vee(sim p wedge q) ) is equivalent to ( A ) B. 9 ( c cdot p wedge q ) D. |
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176 | The disjunction of the statements, “lt is raining; The sun is shining” is A. It is raining and the sun is shining B. It is raining or the sun is shining c. It is raining and the sun is not shining D. It is not raining or the sun is not shining |
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177 | The contrapositive of the statement ‘I go to school if it does not rain’ is: A. If it rains, I do not go to school. B. If I do not go to school, it rains. c. If it rains, I go to school. D. If i go to school, it rains |
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178 | If ( boldsymbol{x}+mathbf{4}=mathbf{8}, ) then ( boldsymbol{x}=mathbf{4}, ) Inverse of the statement is- A. If ( x+4=8 ), then ( x neq 4 ) B. If ( x+4 neq 8 ), then ( x neq 4 ) c. If ( x+4 neq 8 ), then ( x=4 ) D. none of the above |
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179 | Mary says “The number I am thinking is divisible by 2 or it is divisible by ( 3 ” ). This statement is false if the number Mary is thinking of is ( A cdot 6 ) B. 8 ( c cdot 11 ) D. 15 |
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180 | Write the negation of the following statement and check whether the resulting statement is true. The sum of 2 and 5 is 9 |
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181 | State whether the following sentences are always true, always false or ambiguous.Justify your answer. There are 27 days in a month. |
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182 | 61. The statement ~(po~q) is : (JEEM 20141 (a) a tautology (b) a fallacy © eqivalent to p q (d) equivalent to – p a |
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183 | Which of the following is logically equivalent to ( sim(sim p Rightarrow q) ? ) A ( cdot p wedge q ) В . ( p wedge sim q ) ( mathrm{c} cdot sim p wedge q ) D ( . sim p wedge sim q ) |
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184 | Write the compound statement, “If ( mathrm{p} ) then ( q ) and if ( q, ) then ( p^{prime prime} ) in symbolic form. A ( (p wedge q) wedge(q wedge p) ) a ( (p wedge q) wedge(q wedge p) ) в. ( (p Longrightarrow q) vee(q Longrightarrow p) ) c. ( (q Longrightarrow p) wedge(p Longrightarrow q) ) D. ( (p wedge q) vee(q wedge p) ) |
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185 | Tell whether the following is certain to happen, impossible can happen but not certain. You are older today than yesterday. |
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186 | Assertion ( P(n)=n^{2}+n+1 ) is an odd natural number ( forall n in N ) Reason If 1 is added to an even number then it becomes an odd number A. Both (A) & (R) are individually true & (R) is correct explanation of (A), B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A) c. (A)is true but (R) is false D. (A)is false but (R) is true |
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187 | Write the negative of the following statement: All the students completed their homework. |
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188 | Which of the following is a statement? A. I like lions B. Logic is an interesting subject C. A triangle is a circle and 10 is a prime number D. None of these. |
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189 | What is the truth value of the statement ( mathbf{2} times mathbf{3}=mathbf{6} ) or ( mathbf{5}+mathbf{8}=mathbf{1 0} ? ) A. True B. False C. Neither True nor False D. Cannot be determined |
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190 | Construct the truth table for the statement ( (boldsymbol{p} wedge boldsymbol{q}) vee boldsymbol{r} ) |
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191 | State whether the following statements are true or false. Give reasons for your answers. Square numbers can be written as the sum of two odd numbers. |
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192 | The negation of the statement ( (boldsymbol{p} rightarrow ) ( boldsymbol{q}) wedge boldsymbol{r} ) is ( mathbf{A} cdot p wedge sim q vee sim r ) В ( .(sim p wedge q) wedge(sim r) ) c. ( (p wedge sim q) wedge(r) ) D. ( (p wedge sim q) wedge(sim r) ) |
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193 | The statement ” ( x>5 ) or ( x<3 " ) is true, if x equals ( mathbf{A} cdot mathbf{1} ) B. 3 ( c cdot 4 ) D. |
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194 | The compound statement, “If you want to top the school, then you do not study hard” is equivalent to A. “If you want to top the school, then you need to study hard” B. “If you will not top in the school, then you study hard”” c. “If you study hard, then you will not top the school”. D. “If you do not study hard, then you will top in the school” |
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195 | Negation of ( boldsymbol{q} vee sim(boldsymbol{p} wedge boldsymbol{r}) ) is A ( cdot sim q wedge sim(p wedge r) ) В . ( q wedge(p wedge r) ) ( mathbf{c} cdot sim q vee(p wedge r) ) D. None of these |
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196 | The truth value of the statement, “We celebrate our Independence day on 15 August”, is A . T B. F C. neither T nor F D. Cannot be determined |
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197 | Write the inverse of the statement- If you do not drink your milk, you will not be strong. A. If you are strong, then you drink your milk B. If you do not drink your milk, then you are strong C. If you drink your milk, then you are strong D. None of the above |
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198 | If ( p rightarrow(q vee r) ) is false, then the truth values of ( p, q, r ) are respectively ( mathbf{A} cdot mathbf{T}, mathbf{F}, mathbf{F} ) B. F, F, F c. F, T, T D. Т, т, ( F ) |
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199 | Let ( P(n) ) denote the statement that ( boldsymbol{n}^{2}+boldsymbol{n} ) is odd. It is seen that ( boldsymbol{P}(boldsymbol{n}) Rightarrow ) ( P(n+1), P(n) ) is true for all ( mathbf{A} cdot n>1 ) B. c ( . n>2 ) D. None of these |
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200 | If ( p, q, r ) are simple proportions with truth values ( T, F, T, ) then the truth value of ( (sim p vee q) wedge sim r Rightarrow p ) is A. True B. False c. True, if ( r ) is false D. True, if ( q ) is true |
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201 | Which of the following is a statement? A. Open the door. B. Do your home work. c. Hurrah! We have won the match. D. Two plus two is five |
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202 | The contrapositive of “if in a triangle ( A B C, A B=A C, ) then ( angle B=angle C^{prime prime}, ) is ( mathbf{A} cdot ) If in a triangle ( A B C, angle B=angle C, ) then ( A B=A C ) B. If in a triangle ( A B C, A B neq A C ), then ( angle B neq angle C ). C. If in a triangle ( A B C, angle B neq angle C, ) then ( A B neq A C ). D. If in a triangle ( A B C, angle B neq angle C, ) then ( A B=A C ). |
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203 | Write the converse and contrapositive of the statement “If two traingles are congruent, then their areas are equal.” |
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204 | Determine the contrapositive of the following statement: If she works, she will earn money |
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205 | Re write each of the following statements in the form “p if and only if ( q^{prime prime} ) (i) ( p: ) If you watch television then your mind is free and if your mind is free then you watch television (ii) ( q: ) For you to get an A grade it is necessary and sufficient that you do all the homework regularly (iii) ( r: ) If a quadrilateral is equiangular then it is a rectangle and if a quadrilateral is a rectangle then it is equiangular |
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206 | Consider the following two statements: ( P: ) If 7 is an odd number, then 7 is divisible by 2. Q: If 7 is a prime number, then 7 is an odd number If ( V_{1} ) is the truth value of the contrapositive of ( mathrm{P} ) and ( V_{2} ) is the truth value of contrapositive of ( Q, ) then the ordered pair ( left(V_{1}, V_{2}right) ) equals: A. ( (F, F) ) в. ( (T, T) ) c. ( (T, F) ) D. ( (F, T) ) |
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207 | Inverse of the statement “If the triangle with side lengths ( a, b, c ) is a right triangle, then ( a^{2}+b^{2}=c^{2} ) A ( cdot ) If ( a^{2}+b^{2} neq c^{2} ) then the triangle with side lengths ( a, b, c ) is not a right triangle. B. If ( a^{2}+b^{2}=c^{2} ) then the triangle with side lengths ( a, b, c ) is a right triangle C. If the triangle with side lengths ( a, b, c ) is a not right triangle, then ( a^{2}+b^{2} neq c^{2} ) D. None of the above. |
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208 | If ( p ) ‘s truth value is ( T ) and ( q^{prime} ) s truth value is ( F, ) then which of the following have the truth value ( T ) ? (i) ( p vee q ) (ii) ( sim boldsymbol{p} vee boldsymbol{q} ) ( (text { iii) } p vee(sim q) ) ( (text { iv }) p wedge(sim q) ) A ( cdot(i),(text { ii) }, ) (iii) B. (i), (iii), (iv) c. (i), (ii), (iv) D. (ii), (iii), (iv) |
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209 | The contrapositive of ( boldsymbol{p} rightarrow(sim boldsymbol{q} rightarrow sim boldsymbol{r}) ) is equivalent to ( mathbf{A} cdot(sim q wedge r) rightarrow sim p ) В ( cdot(q wedge sim r) rightarrow sim p ) c. ( p rightarrow(sim r vee q) ) D. ( p wedge(q vee r) ) |
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210 | The contrapositive of the following statement, “If the side of a square doubles, then its area increases four times” is: A. If the area of a square increases four times, then its side is not doubled B. If the area of a square increases four times, then its side is doubled C. If the area of a square does not increase four times then its side is not doubled D. If the side of a square is not doubled, then its area does not increase four times |
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211 | Using truth tables, examine whether the statement pattern ( (boldsymbol{p} wedge boldsymbol{q}) vee(boldsymbol{p} wedge boldsymbol{r}) ) is a tautology, contradiction or contingency |
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212 | Show that the statement ( p: ) “If ( x ) is a real number such that ( x^{3}+ ) ( 4 x=0 ) then ( x ) is ( 0^{prime prime} ) is true by (i) direct method (ii) method of contradiction (iii) method of contrapositive |
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213 | The contrapositive of “if in a triangle ( A B C, A B>A C, ) then ( angle C>angle B^{prime prime}, ) is ( mathbf{A} cdot ) If in a triangle ( A B C, angle C>angle B, ) then ( A B>A C ) B. If in a triangle ( A B C, A B not ) # A then ( angle C Varangle angle B ). C. If in a triangle ( A B C, angle C Varangle angle B, ) then ( A B>A C ). D. If in a triangle ( A B C, angle C Varangle angle B, ) then ( A B Varangle A C ). |
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214 | Write the given statement using numbers, literals and signs of basic operations. State what each letter represents. The selling price equals the sum of the cost price and the profit. |
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215 | Check the validity of the following statement: ( boldsymbol{p}: boldsymbol{6} boldsymbol{0} ) is a multiple of ( boldsymbol{3} ) and ( boldsymbol{5} ) A. True B. False |
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216 | Assertion ( (A): ) Let ( n in N ) ( boldsymbol{p}(boldsymbol{n})=boldsymbol{n}(boldsymbol{n}+1) ) is an even number Reason (R): Product of two consecutive natural numbers is even. A. Both (A) & (R) are individually true & (R) is correct explanation of (A), B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A) c. (A)is true but (R) is false D. (A)is false but (R) is true |
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217 | In the following letter sequence, some of the letters are missing. These are given in order as one of the alternatives below Choose the correct alternative. ( boldsymbol{alpha} boldsymbol{beta}_{-} boldsymbol{alpha} boldsymbol{alpha}_{-} boldsymbol{beta} boldsymbol{beta} boldsymbol{beta}_{-} boldsymbol{alpha} boldsymbol{alpha} boldsymbol{alpha} boldsymbol{a}_{-} boldsymbol{beta} boldsymbol{beta} boldsymbol{beta} ldots ) ( mathbf{A} cdot alpha beta beta alpha ) B. ( beta alpha beta alpha ) ( mathrm{c} cdot alpha alpha alpha beta ) ( mathbf{D} cdot alpha beta alpha beta ) |
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218 | Which of the following is the negation of the statement, For all odd primes ( boldsymbol{p}<boldsymbol{q} ) there exists positive non-primes ( r<s ) such that ( p^{2}+q^{2}=r^{2}+s^{2} ) A. For all odd primes ( p<q ) there exists positive nonprimes ( r<s ) such that ( p^{2}+q^{2}=r^{2}+s^{2} ) B. There exists odd primes ( p<q ) such that for all positive non-primes ( r<s, p^{2}+q^{2}=r^{2}+s^{2} ) C. There exists odd primes ( p<q ) such that for all positive non-primes ( r<s, p^{2}+q^{2} neq r^{2}+s^{2} ) D. For all odd primes ( p<q ) and for all positive nonprimes ( r<s, p^{2}+q^{2} neq r^{2}+s^{2} ) |
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219 | 76. For any two statements p and q, the negation of the expression pvpaq) is: [JEEM 2019-9 April (a) ~PA – – . (b) PA (c) paq d) – pv~9 |
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220 | Contrapositive of the statement “if two number are not equal then their square are not equal is ; A. If the squares of two number are equal, then the number are not equal B. If the squares of two number are equal, then the number are equal C. If the square of two number are not equal then number are equal D. If the square of two number are not, equal, then the number are not equal |
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221 | Which of the following is NOT equivalent to ( boldsymbol{p} rightarrow boldsymbol{q} ? ) A. ponly if q B. q is necessary for ( p ) c. q only if ( p ) D. p is sufficient for ( q ) |
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222 | Which statement represents the inverse of the statement “lf it is snowing, then Skeeter wears a sweater.”? A. If Skeeter wears a sweater, then it is snowing B. If Skeeter does not wear a sweater, then it is not snowing. C. If it is not snowing, then Skeeter does not wear a sweater D. If it is not snowing, then Skeeter wears a sweater |
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223 | Given are three positive integers ( a, b ) and ( c . ) Their greatest common divisor is ( D ; ) their least common multiple is ( M ) Then, which two of the following statements are true? (1) The product ( M D ) cannot be less than abc (2) The product ( M D ) cannot be greater than abc (3) ( M D ) equals ( a b c ) if and only if ( a, b, c ) are each prime (4) ( M D ) equals ( a b c ) if and only if ( a, b, c ) are relatively prime in pairs (This means: no two have a common factor greater than ( 1 . ) ( mathbf{A} cdot 1,2 ) в. 1,3 c. 1,4 D. 2,3 E .2,4 |
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224 | State the converse and contrapositive of each of the following statements: (i) ( p: A ) positive integer is prime only if it has no divisors other than 1 and itself (ii) ( q: ) I go to a beach whenever it is a sunny day (iii) ( r: ) If it is hot outside then you feel thirsty |
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225 | Write the converse and contropositive of If a parallelogram is a square, then it is a rhombus’. |
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226 | The contrapositive of : “If two triangles are congruent then they are similar” is A. If two triangles are similar then they are congruent B. If two triangles are not congruent then they are not similar C. If two triangles are not similar then they are not congruent D. None |
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227 | Consider the. following compound statementt (i) Mumbai is the capital of Rajasthan or Maharashtra, (ii) ( sqrt{3} ) is a rational number or an irrational number, (iii) 125 is a multiple of 7 or 8 (iv) A rectangle is a quadrilateral or a regular hexagon. Which of the above statements is not true? A. (i) B. (ii) c. (iii) ( D cdot(mid v) ) |
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228 | Which of the following is a statement? A. Rani is a beautiful girl. B. Shut the door. c. Yesterday was Friday. D. If its raining then there must be cloud in the sky |
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229 | How many buses are there for Suryapet from Hyderabad? ( mathbf{A} cdot mathbf{7} ) B. 17 c. 12 D. 15 |
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230 | 51. Consider the following statements [2011] P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as (a) ~(Q (P^~R)) (b) ~QH-PAR (c) ~(PA~R) HQ (d) ~PAQ H-R) |
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231 | Which is logically equivalent to “If today is Sunday Matt cannot play hockey”? A. Today is Sunday and Matt can play hockey B. If Matt plays hockey then today is not Sunday c. Today is Sunday and Matt cannot play hockey D. Today is not Sunday if and only if Matt plays hockey |
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232 | Which of the following statements is the converse of “You cannot skateboard if you do not have a sense of balance.”? A. If you cannot skateboard, then you do not have a sense of balance B. If you do not have a sense of balance, then you cannot skateboard. c. If you skateboard, then you have a sense of balance D. None of these |
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233 | The inverse of the statement ( (p wedge sim ) ( boldsymbol{q}) rightarrow boldsymbol{r} ) is A. ( (p vee sim q) rightarrow sim r ) в. ( (sim p wedge sim q) rightarrow sim r ) c. ( (sim p vee q) rightarrow sim r ) D. None of these. |
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234 | Which of the following is logically equivalent to ( sim(sim p Rightarrow q) ? ) A ( cdot p wedge q ) В . ( p wedge sim q ) ( mathrm{c} cdot sim p wedge q ) D ( . sim p wedge sim q ) |
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235 | The contrapositive of the statement “If it is raining, then I will not come”, is : A. If I will come, then it is not raining. B. If I will not come, then it is raining. c. If 1 will come, then it is raining D. If I will not come, then it is not raining |
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236 | Let ( p, q ) and ( r ) be any three logical statements. Which one of the following is true? ( mathbf{A} cdot sim[p wedge(sim q)] simeq(sim p) wedge q ) В . ( (p vee q) wedge(sim r) equiv(sim p) vee(sim q) vee(sim r) ) c. ( sim[p vee(sim q)] equiv(sim p) wedge q ) D . ( [p wedge(sim q)] equiv(sim p) wedge sim q ) E . ( [p wedge(sim q)] equiv p wedge q ) |
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237 | ( 7 neq 10 . ) Choose the option that expresses the statement using the correct connective. A ( . sim(7=10) ) В. ( (7 neq 10) ) c. ( sim(-7=10) ) D. ( (-7 neq-10) ) |
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238 | Which of the following is the inverse of the proposition : ‘If a number is a prime then it is odd”? A. If a number is not a prime then it is odd B. If a number is not a prime then it is not odd c. If a number is not odd then it is not prime D. If a number is odd then it is a prime |
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239 | The statement ( boldsymbol{p} rightarrow(boldsymbol{q} rightarrow boldsymbol{p}) ) is equivalent to A ( cdot p rightarrow(p wedge q) ) в. ( p rightarrow(p leftrightarrow q) ) c. ( p rightarrow(p rightarrow q) ) D. ( p rightarrow(p vee q) ) |
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240 | ( sim p wedge q ) is logically equivalent to ( mathbf{A} cdot p rightarrow q ) в. ( q rightarrow p ) ( mathbf{c} cdot sim(p rightarrow q) ) ( mathbf{D} cdot sim(q rightarrow p) ) |
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241 | Consider Statement-1 : (p^-9)^(-p^q) is a fallacy. Statement-2: (p 9) (-9 -p) is a tautology. [JEE M 2013] (a) Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-I. (c) Statement-1 is true; Statement-2 is false. (d) Statement-1 is false; Statement-2 is true. 58 AL the studente falace nerformed noorly in |
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242 | 61. The statement p (a) a tautology (b) eqivalent to p 2. Let A and nu ~9) 1: [JEE M 2014) a fallacy q (d) equivalent to – p 9 elemento |
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243 | State the following statement is True or False If Susan does not like spinach then the truth value of the statement “Susan |
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244 | Write the converse and contrapositive of the statement “lf the two lines are parallel then they do not intersects in the same plane”. |
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245 | Let ( S ) be non-empty subset of ( boldsymbol{R} ) then consider the following statement “Every number ( x in S ) is an even number.” Negation of the statement will be |
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246 | State whether the following sentences are always true, false or ambiguous. Justify your answer. The earth is the only planet where life exist. | 11 |

247 | ( sim[(sim p) wedge q] ) is logically equivalent to A ( . sim(p vee q) ) В ( . sim[p wedge(sim q)] ) C ( . p wedge(sim q) ) D. ( p vee(sim q) ) E ( .(sim p) vee(sim q) ) |
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248 | Statement ( 1: sim(mathbf{p} leftrightarrow sim mathbf{q}) ) is equivalent to ( mathbf{p} leftrightarrow mathbf{q} ) Statement ( 2: sim(mathbf{p} leftrightarrow sim q) ) is a tautology A. Both Statement 1 and Statement 2 are true and Statement 2 is a correct explanation for statement 1 B. Both Statement 1and Statement 2 are true and Statement 2 is not a correct explanation for Statement 1 C. Statement 1 is true but statement 2 is false D. Statement 1 is false but Statement 2 is true |
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249 | The contrapositive of ( (boldsymbol{p} vee boldsymbol{q}) Rightarrow boldsymbol{r} ) is A ( cdot r Rightarrow(p vee q) ) в. ( r Rightarrow(p vee q) ) c. ( r Rightarrow(sim p wedge sim q) ) D. ( p Rightarrow(q vee r) ) |
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250 | The inverse of the propositions ( (p wedge sim ) ( boldsymbol{q}) rightarrow boldsymbol{r} ) is ( mathbf{A} cdot(sim r) rightarrow(sim p) vee q ) в. ( (sim p) vee q rightarrow(sim p) ) c. ( r rightarrow p vee(sim q) ) D. ( (sim p) wedge(sim q) rightarrow r ) |
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251 | If statements ( p, q, r ) have truth values ( T ) ( F, T ) respectively then which of the following statement is true A ( cdot(p rightarrow q) wedge r ) в. ( (p rightarrow q) vee sim r ) C ( .(p wedge q) vee(q wedge r) ) D. ( (p rightarrow q) rightarrow r ) |
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252 | Write the negation of the statement ” ( sqrt{7} ) is irrational” | 11 |

253 | If statement ( boldsymbol{p} rightarrow(boldsymbol{q} vee boldsymbol{r}) ) is true then the truth values of statements ( p, q, r ) respectively ( mathbf{A} cdot mathbf{T}, mathbf{F}, mathbf{T} ) в. F, Т, F ( mathrm{c} cdot mathrm{F}, mathrm{F}, mathrm{F} ) D. all of these |
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254 | State whether the following statements are true or false. Give reasons for your answers. For any real number ( boldsymbol{x}, boldsymbol{x}^{2} geq mathbf{0} ) A. True B. False |
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255 | Which of the following is the inverse of the proposition “If a number is prime, then it is odd”? A. If a number is not prime, then it is odd. B. If a number is not a prime, then it is not odd. c. If a number is not odd, then it is not a prime. D. If a number is not odd, then it is a prime. |
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256 | Logically equivalent statement to ( boldsymbol{p} leftrightarrow boldsymbol{q} ) is ( mathbf{A} cdot(p rightarrow q) wedge(q rightarrow p) ) ( mathbf{B} cdot(p wedge q) vee(q rightarrow p) ) ( mathbf{c} cdot(p wedge q) rightarrow(q vee p) ) D. none of these |
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257 | Which of the following is not a tautology? A. ( p rightarrow(p vee q) ) в. ( (p wedge q) rightarrow p ) c. ( (p vee q) rightarrow(p wedge(sim q)) ) D. ( (p vee sim p) ) |
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258 | “If Tom buys a red skateboard then Amanda buys green in-line skates”. Which statement below is logically equivalent? A. If Amanda does not buy green in-line skates then Tom does not buy a red skateboard B. If Tom does not buy a red skateboard then Amanda does not buy green in-line skates C. If Amanda buys green in-line skates then Tom buys a red skateboard D. If Tom buys a red skateboard then Amanda does not buy green in-line skates |
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259 | ( P rightarrow(q rightarrow r) ) is logically equivalent to A ( cdot(q vee q) rightarrow sim r ) в. ( (p wedge q) rightarrow sim r ) c. ( (p vee q) rightarrow r ) D. ( (p wedge q) rightarrow r ) |
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260 | Which of the following is not proposition? A. 3 is prime. B. ( sqrt{2} ) is irrational. c. Mathematics is interesting D. 5 is an even integer |
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261 | The negative of the statement “he is rich and happy” is given by A. He is not rich and not happy B. He is not rich or not happy c. He is rich and happy D. He is not rich and happy |
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262 | The converse of ( boldsymbol{p} rightarrow(boldsymbol{q} rightarrow boldsymbol{r}) ) is ( mathbf{A} cdot(q wedge sim r) vee p ) в. ( (sim q vee r) vee p ) ( c cdot(q wedge sim r) wedge sim p ) ( p ) D. ( (q wedge sim r) wedge p ) |
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263 | State whether the ” Or” used in the following statements is “exclusive “or” inclusive Give reasons for your answer (i) Sun rises or Moon sets (ii) To apply for a driving licence you should have a ration card or a passport (iii) All integers are positive or negative |
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264 | The contrapositive of the statement “If you believe in yourself and are honest then you will get sucess” is A. If you do not believe yourself and are dishonest then you will not get success. B. If you do not believe yourself and are dishonest then you will get success c. If you get success then you are honest and you also believe in yourself. D. If you will not get success then you don’t not believe in yourself or are not honest |
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265 | Consider the statements (i)Two plus three is five. (ii) Every square is a rectangle. (iii) Sun rises in the east. (iv) The earth is not a star. Which of the above statements have truth value (T) ? A. (i) and (ii) B. (ii) and (iii) c. (iii) and (iv) D. All of these |
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266 | Determine the contrapositive of the following statement: Only If Max studies will he pass the test. |
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