Question

If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.

Options

• T, F, F

• F, T, T

• T, T, T

• F, F, F

Answer 1

If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are T, F, F.

Explanation:

Since (p ∧ ~ r) → (~ p ∨ q) ≡ F

⇒ (p ∧ ~ r) ≡ T and (~ p ∨ q) ≡ F

⇒ p ≡ T, ~ r ≡ T and ~ p ≡ F, q ≡ F

⇒ p ≡ T, q ≡ F, r ≡ F

∴ The truth values of p, q and r are T, F, F respectively.