# Logics – 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

2. p → q is logically equivalent to ________
a) ¬p ∨ ¬q
b) p ∨ ¬q
c) ¬p q
d) ¬p ∧ q

3. p q is logically equivalent to ________
a) ¬q → ¬p
b) q → p
c) ¬p → ¬q
d) ¬p → q

4. ¬ (p ↔ q) is logically equivalent to ________
a) q↔p
b) p↔¬q
c) ¬p↔¬q
d) ¬q↔¬p

5. p q is logically equivalent to ________
a) ¬ (p → ¬q)
b) (p → ¬q)
c) (¬p → ¬q)
d) (¬p → q)

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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

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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)

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)

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

10. ¬ (p ↔ q) is logically equivalent to ________
a) p ↔ ¬q
b) ¬p ↔ q
c) ¬p ↔ ¬q
d) ¬q ↔ ¬p