I think I've got this one, I'd just like someone to check my work(adsbygoogle = window.adsbygoogle || []).push({});

Negate the statement [tex] (\exists! x \in S) P(x) [/tex]

Since [tex] (\exists ! x \in S) P(x) \Longleftrightarrow \{(\exists x \in S) (P(x) \} \wedge \{(\forall x,y \in S) [P(x) \wedge P(y) \longrightarrow x = y \} [/tex]

The negation would be [tex] \sim (\exists ! x \in S) P(x) \Longleftrightarrow \{(\forall x \in S) \sim P(x)\} \wedge \{\exists x,y \in S) \sim [P(x) \wedge P(y) \longrightarrow x = y \} [/tex]

Does this look correct?

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# Negating uniqueness

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