7.2 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. (d) x (Q(x) P(x))

(e) x (Q(x) P(x))

7.5 In the following question, the domain of discourse is the set of employees of a company. Define the following predicates:

A(x): x is on the board of directors E(x): x earns more than $100,000 W(x): x works more than 60 hours per week

Translate the following logical expressions into English: (e) x (E(x) (A(x) W(x)))

(f) x (A(x) E(x) W(x))