If p ∧ ~ q ∧ p ∧ r → ~ p ∨ q is false, then the truth values of p , q and r are respectively

Step-by-step solution

Recall p ⇒ q ≡ F if and only if T ⇒ F ≡ F So, p ∧ ~ q ∧ p ∧ r → ~ p ∨ q Taking Option A   : T ∧ F ∧ T ∧ T → F ∨ T ≡ F ∧ T → T ≡ F → T ≡ T Hence, option A is false. Taking Option B   : F ∧ F ∧ F ∧ F → T ∨ T ≡ F → T ≡ T Hence, option B is false. Taking Option C   : T ∧ T ∧ T ∧ T → F ∨ F ≡ T → F &