Let $D$ be the set $\{1, 2, 3\}$. How many elements are there in $D \times D$?
Consider a predicate logic with one one-argument relation $P(x)$ and one two-argument relation $R(x, y)$, along with constant $a$, with $x, y, a \in D$. Give a model with domain $D$ for which the statement "$\exists x\ R(x, a)$" is false.