This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Logical Equivalences”.

1. 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

View Answer

Explanation: Definition of logical equivalence.

2. p → q is logically equivalent to:

a) ¬p ∨ ¬q

b) p ∨ ¬q

c) ¬p ∨ q

d) ¬p ∧ q

View Answer

Explanation: (p → q) ↔ (¬p ∨ q) is tautology.

3. p ∨ q is logically equivalent to:

a) ¬q → ¬p

b) q → p

c) ¬p → ¬q

d) ¬p → q

View Answer

Explanation: (p ∨ q) ↔ (¬p → q) is tautology.

4. ¬ (p ↔ q) is logically equivalent to:

a) q↔p

b) p↔¬q

c) ¬p↔¬q

d) ¬q↔¬p

View Answer

Explanation: ¬(p↔q)↔(p↔¬q) is tautology.

5. p ∧ q is logically equivalent to:

a) ¬ (p → ¬q)

b) (p → ¬q)

c) (¬p → ¬q)

d) (¬p → q)

View Answer

Explanation: (p ∧ q) ↔ (¬(p → ¬q)) is tautology.

6. 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

View Answer

Explanation: Verify using truth table, all are correct.

7. 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)

View Answer

Explanation: (p ↔ q) ↔ ((p → q) ∧ (q → p)) is tautology.

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

a) p → (q ∧ r)

b) p → (q ∨ r)

c) p ∧ (q ∨ r)

d) p ∨ (q ∧ r)

View Answer

Explanation: ((p → q) ∧ (p → r)) ↔ (p → (q ∧ r)) is tautology.

9. (p → r) ∨ (q → r) is logically equivalent to:

a) (p ∧ q) ∨ r

b) (p ∨ q) → r

c) (p ∧ q) → r

d) (p → q) → r

View Answer

Explanation: ((p → r) ∨ (q → r)) ↔ ((p ∧ q) → r) is tautology.

10. ¬ (p ↔ q) is logically equivalent to:

a) p ↔ ¬q

b) ¬p ↔ q

c) ¬p ↔ ¬q

d) ¬q ↔ ¬p

View Answer

Explanation: (¬ (p ↔ q)) ↔ (p ↔ ¬q) is tautology.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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