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What is the negation of '∀x P(x)'?
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∀x NOT P(x)
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∃x ¬P(x)
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∃x NOT P(x)
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∀x P(x)
That's Correct!
It's Wrong!
The negation of the statement '∀x P(x)' (which reads as "For all x, P(x)") is represented as '∃x ¬P(x)' (which reads as "There exists an x for which P(x) is not true"). In other words, it asserts that it is not the case that every x satisfies the property P; there is at least one x for which P(x) is false.
