If P and Q are two statements, then which of the following compound statement is a tautology?

Step-by-step solution

LHS of all the options are same i.e. ( ( P → Q ) ∧ ~ Q ) ≡ ( ~ P ∨ Q ) ∧ ~ Q ≡ ( ~ P ∧ ~ Q ) ∨ ( Q ∧ ~ Q ) ≡ ~ P ∧ ~ Q (A) ( ~ P ∧ ~ Q ) → Q ≡ ~ ( ~ P ∧ ~ Q ) ∨ Q ≡ ( P ∨ Q ) ∨ Q ≠ tautology (B) ( ~ P ∧ ~ Q ) → ~ P ≡ ~ ( ~ P ∧ ~ Q ) ∨ ~ P ≡ ( P ∨ Q ) ∨ ~ P (C) ( ~ P ∧ ~ Q ) → P ≡ ( P ∨ Q ) ∨ P ≠ Tautology (D) ( ~ P