7.
Solution.
\(P(11)\) is the statement β\(16\cdot 11 + 1\) is evenβ, which is false. Thus the statement \(\forall x P(x)\) is false (for example, 11 is a counterexample). However, we cannot tell anything about \(\exists x P(x)\) since we do not know the truth value of \(P(x)\) for other elements of the domain of discourse. In this case, \(\exists x P(x)\) happens to be true (since \(P(1)\) is true, for example).