Solution
= Solution
The antecedent says that the nonempty domain has \b[at most two elements]: its two witnesses need not be distinct. The consequent says it has exactly one element. Thus
$$
\boxed{\mathcal A\models\psi\iff |A|\ne2.}
$$
One-element structures satisfy both sides; domains of size at least three, including infinite domains, make the antecedent false. The <function> $f$ has no bearing on this condition.