| P | Q | P → Q | Q → P | (P → Q) ∧ (Q → P) | P ↔ Q |
|---|---|---|---|---|---|
| F | F | T | T | T | T |
| T | F | F | T | F | F |
| F | T | T | F | F | F |
| T | T | T | T | T | T |
This formula represents the most basic biconditional relationship in propositional logic. It states that P and Q must have the same truth value - both true or both false. The biconditional is equivalent to the conjunction of two implications (P→Q) ∧ (Q→P), demonstrating that logical equivalence requires mutual implication. This fundamental relation is used to establish definitions and equivalences in formal logical systems.