Predicates P and Q are defined below. The domain of discourse is the set of all positive integers.

P(x): x is prime

Q(x): x is a perfect square (i.e., x = y2, for some integer y)

Indicate whether each logical expression is a proposition. If the expression is a proposition, then give its truth value.

(a)

x Q(x)

(b)

x Q(x) P(x)

(c)

x Q(x) P(3)

(d)

x (Q(x) P(x))

(e)

x (Q(x) P(x))