[3 pt] 16. Select the logical expression that is equivalent to:
"Someone who did not study for the test received an A on the test."
a. $\exists x(A(x)\rightarrow S(x))$
b. $\exists x(\neg S(x) \rightarrow A(x))$
c. $\exists x(\neg S(x) \land A(x))$
d. $\exists x(\neg S(x) \leftrightarrow A(x))$
[4 pt] 17. The domain for variables x and y is the set {1, 2, 3}. The table below gives the values
of P(x, y) for every pair of elements from the domain. For example, P(2, 3) = F because the value
in row 2, column 3, is F.
\begin{tabular}{|c|c|c|c|}
\hline
P & 1 & 2 & 3 \\
\hline
1 & T & T & T \\
2 & T & F & F \\
3 & F & T & F \\
\hline
\end{tabular}
Select all of the statements that are false.
a. $\exists x \forall y P(x, y)$
b. $\forall x \exists y P(x, y)$
c. $\exists y \forall x P(x, y)$
d. $\forall y \exists x P(x, y)$
e. $\exists x \exists y P(x, y)$
f. $\exists y P(2, y)$
g. $\forall y P(1, y)$
h. $\exists y \neg P(1, y)$
