In propositional logic P ↔ Q is equivalent to (Where ~ denotes NOT)

To find which expression is equivalent to P ↔ Q, let's first break down the standard definition of a biconditional (two-way) implication.

By definition: P ↔ Q ≡ (P → Q)∧(Q → P)

Using the implication elimination rule (A → B ≡ ¬A ∨ B), we can rewrite both individual conditional statements:

P → Q ≡ ¬P ∨ Q

Q → P ≡ ¬Q ∨ P

Substituting these back into the conjunction gives:

P → Q ≡ (¬P ∨ Q)∧ (¬Q ∨ P)