Definition. Equivalence of Formulae [000c]
Definition. Equivalence of Formulae [000c]
Two formulas \(F\) and \(G\) are said to be equivalent, written \(F \equiv G\), if they have the same truth value under every interpretation. In other words, for every interpretation \(I\), \(I \models F\) if and only if \(I \models G\).
\[ F \equiv G \iff \forall I (I \models F \iff I \models G) \]