Question

DISCRETE MATHS [ BOOLEANS AND LOGIC] Please answer all

Exercise 1.7.1: Determining whether a quantified statement about the integers is true.

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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.

(c)

∀x Q(x) ∨ P(3)

(d)

∃x (Q(x) ∧ P(x))

(e)

∀x (¬Q(x) ∨ P(x))

Answer 1