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