Question

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

[(∼ p ∧ q) ∧ ∼ r] ∨ [(q → p) → (∼ s ∨ r)]

Answer 1

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

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