 If \(S\) is the function corresponding to ‘sang’, then Mary sang iff—i.e., if and only if—\(S(\textrm{Mary}) = \textbf{T}\). Likewise, someone sang iff: \(S\) maps some individual onto \(\textbf{T}\); that is, for some individual \(x\), \(S(x) = \textbf{T}\). Or using a modern variant of Frege’s original notation, someone sang iff \(\exists x [S(x)]\). The quantifier ‘\(\exists x\)’ is said to bind the variable ‘\(x\)’, which ranges over individual things in a domain of discourse. (For now, assume that the domain contains only people.) If every individual in the domain sang, then \(S\) maps every individual onto the truth value \(\textbf{T}\); or using formal notation, \(\forall x [S(x)]\). A quantifier binds each occurrence of its variable, as in ‘\(\exists x [P(x) \land D(x)]\)’, which reflects the logical form of ‘Someone is both a politician and deceitful’. In this last example, the quantifier combines with a complex functional component that is formed by conjoining two simpler ones.