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- Suppose $X$ is the empty set, and $P(x)$ is the proposition that $x > 0$.
- Is $(\forall x\in X)(P(x))$ true or false?
- Is $(\forall x\in X)(\Not P(x))$ true or false?
- If $X$ is any set and $P(x)$ is a proposition, is $[(\forall x\in X)(P(x))] \implies [(\exists x\in X)(P(x))]$ true?
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