Ex2

Given: \[\begin{split} R &: big > small \end{split}\]

Then: \[\begin{split} & {wp\left({{if\left(x > y\right) \ \{ big, small := x, y \}} \ {else \ \{ big, small := y, x \}}}, R\right)} \\ {\ ({\mathbf{§4}})} \iff & (x > y \to {wp\left(big, small := x, y, R\right)}) {\ \land \ }(x \leq y \to {wp\left(big, small := y, x, R\right)})\\ {\ ({\mathbf{§1}})} \iff & (x > y \to x > y) {\ \land \ }(x \leq y \to x < y)\\ \iff & x \leq y \to x < y \\ \end{split}\]

This is not true for all \(x, y \in \mathbb{Z}\), specifically when \(x = y\). Therefore: \[\begin{split}Q &= x \neq y\\ \end{split}\]