Question

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

∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)

Answer 1

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

∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)
≡ ∼ [(∼ T ∧ F) ∨ (F → ∼ T)] ↔ (T ∧ F)
≡ ∼ [(F ∧ F) ∨ (F → F)] ↔F
≡ ∼ (F ∨ T) ↔ F
≡ ∼ T ↔ F
≡ F ↔ F ≡ T
Hence the truth value of the given statement is true.