Chapter 1 - Section 1.8 - Proof Methods and Strategy - Supplementary Exercises - Page 112: 22

To make the statement true the domain for the given quantifiers is {$0,1$}Find a domain.

Solution: $\exists x \exists y[x \neq y \wedge \forall z((z=x) \wedge(z=y))]$ expresses that there exists two different elements $x$ and $y$ in the domain and that all elements are equal to either $x $ or $y $. The statement is then true if the domain contains exactly $2$ distinct elements. For example: {0,1}