A two-element model of $\phi$ would be a finite model with even size, contrary to the defining property established in part (b). Every model of $\phi$ therefore has size other than two, and the preceding interpretation of $\psi$ gives $\boxed{\{\phi\}\models\psi}$. This includes infinite models, since the antecedent of $\psi$ is false there.


Solution

Past exam of the logic and set theory course of the University of Oxford / 2011 / A / 2 / d / ii / Solution

 Solution (source code)