discrete math

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Express the quantification:

Existential(!)x P(x)

using universal quantifications, existential quantification and logical expressions. For sake of typing this question, I'm going to let "E" be the existential quantifier, "A" be the universal quantifier", and "^" means "and":

so far I have:

Ex(P(x) ^ Ay --> P(y))

But I have no idea if this is actually correct! I really appreciate your help!

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