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I have to prove the following using set equivalence rules.

$A\cap(B-C) = (A - B) \cap(A - C)$

I can only use the Distributivity law with AND and OR as far as I can tell.

I think I can go ahead with the proof if I can assume that

$(B-C) = B\cap\overline{C}$

but I can't find this in the set rules... what is the name of this step I'm taking??

So is this a definition, am I allowed to use it, or is there any other way of proving this equation just using set equivalence rules?

MrX
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1 Answers1

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This is the set difference law. You can see that for both sides, it is $\{b\in B|b\not\in C\}$

Christopher Liu
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