Discrete Structure (DS) MCQs with answers Page - 12

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Q. 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 don’t 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 over confident
  • (C) If you don’t know the rules or are overconfident you lose the game.
  • (D) If you know the rules and are overconfiden t then you win the game.

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Q. A sufficient condition that a triangle T be a right triangle is that a2 + b2 = c2. An equivalent statement is

  • (A) If T is a right triangle then a2 + b2 = c2.
  • (B) If a2 + b2 = c2 then T is a right triangle.
  • (C) If a2 + b2 6= c2 then T is not a right triangle.
  • (D) T is a right triangle only if a2 + b2 = c2.

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Q. Which of the following is the inverse of the statement: " If I eat a mango than I do not drink milk".

  • (A) I drink milk only if I do not eat a mango
  • (B) If I don’t eat a mango then I drink milk
  • (C) If I do not drink milk then I eat mango
  • (D) None

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Q. If p= It is hot, and q= It is sultry, which of the following sentences in the appropriate version for the symbolic expression: -p٨ q

  • (A) If it is sultry then it is hot
  • (B) It is sultry only if it is hot
  • (C) It is sultry and it is not hot
  • (D) None

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Q. which of the following is the contrapositive of the statement: " A quadrilateral is a square only if it is both rectangle and a rhombus".

  • (A) If a rectangle is not a a rhombus it is not a square
  • (B) If a rhombus is not rectangle it is not a square
  • (C) If a quadrilateral is neither a rectangle nor a rhombus then it is not a square
  • (D) None

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Q. For a conditional statement p===>q, which of the following is incorrect.

  • (A) Converse of the inverse is its contrapositive
  • (B) contrapositive of the converse is its inverse
  • (C) Inverse of the contrapositiv e is its converse
  • (D) None

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Q. Which of the following is equivalent to p==>q

  • (A) ~xp٨q
  • (B) pV~q
  • (C) ~xpVq
  • (D) pV~q

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Q. Equivalent inverse of p==>q is

  • (A) ~xp٨q
  • (B) pV~q
  • (C) ~xpVq
  • (D) pV~q

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Q. Converse of p==>q is

  • (A) ~xp٨q
  • (B) pV~q
  • (C) ~xpVq
  • (D) pV~q

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Q. the truth table for exclusive disjunction will be

  • (A) tautology
  • (B) Contradiction
  • (C) Logical equivalent
  • (D) p or q but not both

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