Question

If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.

विकल्प

• F, F

• T, F

• T, T

• F, T

Answer 1

If p ↔ (~ p → q) is false, then the truth values of p and q are respectively F, T.

Explanation:

The truth value of statement p ↔ (~ p → q) is F

∴ p ≡ T and (~ p → q) ≡ F or

p ≡ F and (~ p → q) ≡ T

If p ≡ T, then (~ p → q) ≡ F implies (F → q) ≡ F, which is not possible for any value of q.

Therefore, we get p = F and (~ p → q) ≡ T

∴ p ≡ F and q ≡ T