If p and q are two statements, then which of the following statements is not equivalent to p ⇔ p ⇒ q ?

Step-by-step solution

p q p ⇒ q p ⇔ p ⇒ q T T T T T F F F F T T F F F T F ⇒ p ⇔ p ⇒ q ≡ p ∧ q ⇒ A is true Now, q ⇔ q ⇒ p ≡ p ∧ q ≡ p ∧ q ⇒ q ⇒ p ⇒ q ≡ p ∧ q ⇒ C is true Now, common between p ⇔ q & p ∨ q is p ∧ q ⇒ p ⇔ q ∧ p ∨ q ≡ p ∧ q ⇒ B is correct Now, ~ q ⇒ p ∧ p ⇒ ~ q ≡ q ∨ p ∧ ~ p ∨ ~ q = Only p or only q ≡ ~ p ⇔ q