The domain for this problem is a set {a, b, c, d}. The table below shows the value of three predicates for each of the elements in the domain. For example, Q(b) is false because the truth value in row b, column Q is F. P Q R a T T F b T F F c T F F d T F F

Which statements are true? Justify your answer. (c) x Q(x)

(d) x Q(x)

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

P(x): x is even T(x, y): 2x = y E(x, y, z): xy = z

Indicate whether each logical expression is a proposition. If the expression is a proposition, then give its truth value. (b) P(3)

(c) T(5, 32)