Discrete Mathematics MCQs with answers Page - 6

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Q. Which of the arguments is not valid in proving sum of two odd number is not odd.

  • (A) 3 + 3 = 6, hence true for all
  • (B) 2n +1 + 2m +1 = 2(n+m+1) hence true for all
  • (C) all of the mentioned
  • (D) none of the mentioned

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Q. A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as

  • (A) direct proof
  • (B) contrapositive proofs
  • (C) vacuous proof
  • (D) proof by cases

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Q. A proof that p → q is true based on the fact that q is true, such proofs are known as

  • (A) direct proof
  • (B) contrapositive proofs
  • (C) trivial proof
  • (D) proof by cases

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Q. In the principle of mathematical induction, which of the following steps is mandatory?

  • (A) induction hypothesis
  • (B) inductive reference
  • (C) induction set assumption
  • (D) minimal set representation

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Q. For m = 1, 2, …, 4m+2 is a multiple of is known as

  • (A) lemma
  • (B) corollary
  • (C) conjecture
  • (D) none of the mentioned

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Q. For any integer m>=3, the series 2+4+6+… +(4m) can be equivalent to

  • (A) m2+3
  • (B) m+1
  • (C) mm
  • (D) 3m2+4

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Q. For every natural number k, which of the following is true?

  • (A) (mn)k = mknk
  • (B) m*k = n + 1
  • (C) (m+n)k = k + 1
  • (D) mkn = mnk

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Q. For any positive integer m is divisible by 4.

  • (A) 5m2 + 2
  • (B) 3m + 1
  • (C) m2 + 3
  • (D) m3 + 3m

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Q. What is the induction hypothesis assumption for the inequality m ! > 2m where m>=4?

  • (A) for m=k, k+1!>2k holds
  • (B) for m=k, k!>2k holds
  • (C) for m=k, k!>3k holds
  • (D) for m=k, k!>2k+1 holds

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