Answer to Question #269470 in Discrete Mathematics for Mao

Question

Suppose that the domain of the predicateP(x) consists of −2, −1, 0, 1, and2. Write out each

of the following predicate logic formulas in propositional logic formulas using disjunctions, conjunctions,

negations, or their combinations.

Answer 1

Suppose that the domain of the propositional function P(x) consists of the integers -2,-1,0,1 and 2. Write out each of these propositions using disjunctions, conjunctions and negations.

a) $\exists x P(x)$ So it says that there exists an x for which P(x) is true.

Then $P(-2) \vee P(-1) \vee P(0) \vee P(1) \vee P(2)$

b) $\forall x P(x)$ Here it says that P(x) is true for every x.

Then $P(-2) \wedge P(-1) \wedge P(0) \wedge P(1) \wedge P(2)$

c) $\exists x \neg P(x)$