Question

$\lnot \forall x P(x) \models \forall x \lnot P(x)$
$P(x) : x$ is divisible by 2 or $P(x) : x$ is a dog. or $P(x) can be anything.

I want to show the following sequents are not valid ..Isn't the following sequents equal or the first sequent the whole negation of the statement and the second sequent is the negation of the $P(x)$ .. Can anybody explain this with examples?

No correct solution

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