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- Thread starter Mr Davis 97
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fresh_42

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Yes, because

The case true and true cannot occur, since either there are many or none at all, which cannot both be true. So the negation of ##\exists !## can be expressed by an exclusive or, sometimes noted as ##\dot{\vee}##.

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Math_QED

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The last one is a true statement if either the existence fails, or the uniqueness.

The former means that there just isn't an x such that P(x) holds, the latter means that two different ones can be found such that the statement holds and this is precisely what the logic describes (because there is no x such that P(x) holds is equivalent with saying that for all x P(x) does not hold)

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