 The existence of a choice function \(f:\{X,Y\} \rightarrow \{0,1\}\) choosing an element from \(X\) and \(Y\) would imply \((A \vee \neg A)\). For if \(f(X)\neq f(Y)\), it follows that \(X\neq Y\), and hence \(\neg A\), whereas \(f(X)=f(Y)\) implies \(A\). Therefore a choice function for \(\{X,Y\}\) cannot exist. 