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How to interpret the set $\{x\mid x \in A \implies x \in B \}$?

I've seen it in exercises from a few texts, but it isn't obvious to me. Thanks.

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    @simplicity I doubt it. That notation makes it seem like $A\subset B$ which implies the set is just $A$ whereas in the original notation it just has to make sense to take the intersection.2011-12-27

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This (unconventionally) defines the set $B\cup(A^c).$ Hint: the assertion $P\implies Q$ is equivalent to $Q\lor(\lnot P)$.

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    @ndroock1 Did you notice the link in my previous comment?2015-09-30