If P and Q are two statements, then which of the following compound...

LHS of all the options are same i.e. $( ( P \to Q ) ∧ ~ Q )$

$≡ ( ~ P ∨ Q ) ∧ ~ Q$

$≡ ( ~ P ∧ ~ Q ) ∨ ( Q ∧ ~ Q )$

$≡ ~ P ∧ ~ Q$

(A) $( ~ P ∧ ~ Q ) \to Q$

$≡ ~ ( ~ P ∧ ~ Q ) ∨ Q$

$≡ ( P ∨ Q ) ∨ Q \ne$ tautology

(B) $( ~ P ∧ ~ Q ) \to ~ P$

$≡ ~ ( ~ P ∧ ~ Q ) ∨ ~ P$

$≡ ( P ∨ Q ) ∨ ~ P$

(C) $( ~ P ∧ ~ Q ) \to P$

$≡ ( P ∨ Q ) ∨ P \ne$ Tautology

(D) $( ~ P ∧ ~ Q ) \to ( P ∧ Q )$

$≡ ( P ∨ Q ) ∨ ( P ∧ Q ) \ne$ Tautology