2.10 For the following wfs and for the given interpretations, indicate for
what values the wfs are satisfied (if they contain free variables) or whether
they are true or false (if they are closed wfs).
(i) $A_1^2(f_1^2(x_1, x_2), a_1)$
(ii) $A_1^2(x_1, x_2) \implies A_1^2(x_2, x_1)$
(iii) $(\forall x_1)(\forall x_2)(\forall x_3)(A_1^2(x_1, x_2) \land A_1^2(x_2, x_3) \implies A_1^2(x_1, x_3))$
(a) The domain is the set of positive integers, $A_1^2(y, z)$ is $y \ge z$, $f_1^2(y, z)$ is
y \cdot z, and $a_1$ is 2.
(b) The domain is the set of integers, $A_1^2(y, z)$ is $y = z$, $f_1^2(y, z)$ is $y + z$, and
$a_1$ is 0.
(c) The domain is the set of all sets of integers, $A_1^2(y, z)$ if $y \subseteq z$, $f_1^2(y, z)$ is
$y \cap z$, and $a_1$ is the empty set $\emptyset$.
