Discrete Mathematics MCQs with answers Page - 5

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Q. Let P: I am in Delhi.; Q: Delhi is clean.; then q ^ p(q and p) is?

  • (A) delhi is clean and i am in delhi
  • (B) delhi is not clean or i am in delhi
  • (C) i am in delhi and delhi is not clean
  • (D) delhi is clean but i am in mumbai

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Q. Let P: This is a great website, Q: You should not come back here. Then ‘This is a great website and you should come back here.’ is best represented by?

  • (A) ~p v ~q
  • (B) p ∧ ~q
  • (C) p v q
  • (D) p ∧ q

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Q. Let P: We should be honest., Q: We should be dedicated., R: We should be overconfident. Then ‘We should be honest or dedicated but not overconfident.’ is best represented by?

  • (A) ~p v ~q v r
  • (B) p ∧ ~q ∧ r
  • (C) p v q ∧ r
  • (D) p v q ∧ ~r

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Q. The compound propositions p and q are called logically equivalent if is a tautology.

  • (A) p ↔ q
  • (B) p → q
  • (C) ¬ (p ∨ q)
  • (D) ¬p ∨ ¬q

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Q. p → q is logically equivalent to

  • (A) ¬p ∨ ¬q
  • (B) p ∨ ¬q
  • (C) ¬p ∨ q
  • (D) ¬p ∧ q

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Q. p ∨ q is logically equivalent to

  • (A) ¬q → ¬p
  • (B) q → p
  • (C) ¬p → ¬q
  • (D) ¬p → q

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Q. ¬ (p ↔ q) is logically equivalent to

  • (A) q↔p
  • (B) p↔¬q
  • (C) ¬p↔¬q
  • (D) ¬q↔¬p

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Q. Which of the following statement is correct?

  • (A) p ∨ q ≡ q ∨ p
  • (B) ¬(p ∧ q) ≡ ¬p ∨ ¬q
  • (C) (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
  • (D) all of mentioned

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Q. p ↔ q is logically equivalent to

  • (A) (p → q) → (q → p)
  • (B) (p → q) ∨ (q → p)
  • (C) (p → q) ∧ (q → p)
  • (D) (p ∧ q) → (q ∧ p)

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Q. (p → q) ∧ (p → r) is logically equivalent to

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

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