A given [[Binary Operation|binary operation]] $\circ$ on the [[Set|set]] $S$ has the [[Inverse Property]] [[Biconditional|if and only if]] [[Universal Quantifier|for any]] $a\in S$, [[Existential Quantifier|there exists]] an element $b\in S$ such that $a\circ b = e$, where $e$ denotes the [[Identity Property|Identity Element]] of $\circ$. $\huge \forall a \in S \exists b \in S : a\circ b =e $