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After drawing a diagram of this statement, I believe it to be false. However, I'm having trouble approaching how to disprove this. Do I try to prove the negation? Or what else can I do?

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    The statement is true (if you're talking about complements)...2012-09-25
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    Ok, yeah, you're right. I just found out that it is true based on Demorgans law. However, I can't use Demorgans law for the proof. So, how do you suggest approaching proving this?2012-09-25
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    There are two ways I'd suggest. One is given by @Babak below, namely show that $(A\cup B)'\subseteq A'\cap B'$ and that $A'\cap B'\subseteq (A\cup B)'$. Another is to use Venn diagrams. Depending on your comfort, you might find one easier than the other.2012-09-25

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