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 ∧ r) ∨ (p ∧ r)]

Answer 1

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

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