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"When is the set statement:

(A\B)⊕(A ∩ B) = A

true? Is it sometimes true, never true, or always true? If sometimes, state the specific cases where it is. A & B are arbitrarily selected sets."

I said it was sometimes, as, it seems if A is empty and B is empty, then A\B is empty, A ∩ B is empty, and so the entire left side is then empty, and so is A. Would that be correct? Further, are there are other cases where this is a true statement?

Thank you for your time. ^^

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    What operation do you denote by $\oplus$ ? Is it symmetric set difference?2012-09-10
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    Are you the same person [who asked this question](http://math.stackexchange.com/questions/193396/when-is-the-set-statement-ab-a-b-true)? If so, why the second account?2012-09-10
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    ⊕ is denoting symmetric difference. Also, yes. New account just because I'm using my Yahoomail account this time, since I couldn't remember which password I used, I just logged in with this one.2012-09-10
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    @JessicaHope Then please stick to either one of the two.2012-09-10
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    Alrighty. I'll do so.2012-09-10

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