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Hi I am learning group theory and encountered this: (B\cap (A\cap B)')\cup (B'\cap (A\cap B)) = B\cap (A'\cup B').

I don't understand how this is true, could someone please show me proof?

Thanks

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    H$a$ve you tried a truth table? It would be huge but I thi$n$k it would be a good exercise in learning equivalence.2011-05-25

1 Answers 1

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Assuming the prime denotes complementation: The second term on the left, B'\cap(A\cap B), is empty, since $B$ and B' are disjoint. That leaves B\cap(A\cap B)'. You can use De Morgan's law (A\cap B)'=A'\cup B' to transform this into the right-hand side.

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    Oh. That's quite nifty. Thanks for the tip! I will say though that, though I'm fairly decent at typesetting my problems sets, I never knew about `$$` and `\begin{align}` until I looked at some of the longer answers.2011-05-28