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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.

  1. $\exists x P(x)$
  2. $\forall x P(x)$
  3. $\exists x \sim p(x)$
  4. $\forall x \sim P(x)$
  5. $\sim \exists x P(x)$
  6. $\sim \forall x P(x)$

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