Chapter 1.4, Problem 18E

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

a) $\exists xP\left(x\right)$

b) $\forall xP\left(x\right)$

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

d) $\forall x\neg P\left(x\right)$

e) $\neg \exists xP\left(x\right)$

f) $\neg \forall xP\left(x\right)$