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Graph (of a function or relation)**

Given a function \(f:X\to Y\) between sets \(X,\:Y\), its graph \(\Gamma_f\subseteq X\times Y\) is the subset of their Cartesian product given by all pairs \((x,f(x)\), i.e. \(\Gamma_f:=\{(x,y)\in X\times Y|x\in x\land y=f(x)\}\). More generally, given a relation \(\mathscr{R}\), its graph is \(\Gamma_\mathscr{R}:=\{(x,y)|x\mathscr{R}y\}\). If \(\mathscr{R}\) is functional or is a relation between sets, then \(\Gamma_\mathscr{R}\) is a set, but in general it may be a proper class.