Question

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(∼ r ↔ p) → ∼ q

Answer 1

Truth values of p and q are T and truth values of r and s are F.

(∼ r ↔ p) → (∼ q) ≡ ( ∼ F ↔ T) → (∼ T)
                             ≡ (T ↔ T) →F
                             ≡ T→ F ≡ F
Hence the truth value of the given statement is false.