Question

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

(q ∧ r) ∨ (∼ p ∧ s)

Answer 1

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

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