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Suppose the domain of the propositional function $P(x,y)$ consists of pairs $x$ and $y$ , where $x$ is 1,2 or 3 and $y$ is 1,2 or 3 . Write out these propositions using disjunctions and conjunctions.

1. $\exists x P(x,3)$
2. $\forall y P(1,y)$
3. $\exists y \sim p(2,y)$
4. $\forall x \sim P(x,2)$
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