Discrete Structure (DS) MCQs with answers Page - 8

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Q. The truth table for (p ∨ q) ∨ (p ∧ r) is the same as the truth table for

  • (A) (p ∨ q) ∧ (p ∨ r)
  • (B) (p ∨ q) ∧ r
  • (C) (p ∨ q) ∧ (p ∧ r)
  • (D) p V q

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Q. Consider the statement, “Either −2 ≤ x ≤ −1 or 1 ≤ x ≤ 2.” The negation of this statement is

  • (A) x < −2 or 2 < x or −1 < x < 1
  • (B) (x < −2 or 2 < x
  • (C) −1 < x < 1
  • (D) x ≤ −2 or 2 ≤ x or −1 < x < 1

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Q. Which of the following statements is FALSE:

  • (A) (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to ∼Q ∧ ∼P
  • (B) (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to Q ∨ P
  • (C) (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to Q ∨ (P ∧ ∼Q)
  • (D) (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to [(P ∨ ∼P) ∧ Q] ∨ (P ∧ ∼Q)

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Q. The number of distinct relations on a set of 3 elements is

  • (A) 8
  • (B) 9
  • (C) 18
  • (D) 512

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Q. How many onto (or surjective) functions are there from an n-element (n => 2) set to a 2-element set?

  • (A) 2n
  • (B) 2n - 1
  • (C) 2n - 2
  • (D) 2(2n – 2)

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Q. How many relations are there on a set with n elements that are symmetric and a set with n elements that are reflexive and symmetric?

  • (A) 2n(n+1)/2 and 2n.3n(n–1)/2
  • (B) 3n(n–1)/2 and 2n(n–1)
  • (C) 2n(n+1)/2 and 3n(n–1)/2
  • (D) 2n(n+1)/2 and 2n(n–1)/2

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Q. The number of functions from an m element set to an n element set is:

  • (A) mn
  • (B) m+n
  • (C) nm
  • (D) m*n

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Q. Let R = {(a, a), (a, b)} be a relation on S = {a, b, c}. Then R is not reflexive and not symmetric.

  • (A) T
  • (B) F
  • (C) ---
  • (D) ---

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Q. Let R = {(a, a), (a, b)} be a relation on S = {a, b, c}. Then R is not transitive.

  • (A) T
  • (B) F
  • (C) ---
  • (D) ---

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Q. The function f : Z → Z given by f (x)= x +1 is a bijection.

  • (A) T
  • (B) F
  • (C) ---
  • (D) ---

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