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Axiom of the Pair Set**

An axiom of Zermelo-Fraenkel set theory which states that, for any two sets \(X,Y\), there exists a set (\(\{X,Y\}\)) whose elements are precisely \(X\) and \(Y\): \(\forall X:\forall Y:\exists Z:\forall a: (a\in Z\Leftrightarrow a=X\lor a=Y)\).