I am trying to prove that A union (B intersection C) = (A union B) intersection (A union C). In other words, proving one of DeMorgan's Laws. I have gotten this far, and not sure if I'm right thus far:(adsbygoogle = window.adsbygoogle || []).push({});

Let x belong to A union (B intersection C). Then x is in either A or in (B intersection C).

Case 1: x belongs to A.

In this case, x belongs to (A union B) and x belongs to (A union C).

Case 2: x belongs to (B intersection C).

In this case, x belongs to either (A union B) or (A union C).

So x belongs to ((A union B) intersection (A union C)) union ((A union B) union (A union C)).

((A union B) union (A union C)) can be rewritten as (using associative property):

(A union B union A union C), or simply (A union B union C).

What do I do now? Thank you.

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# Proof Involving Binary Operators

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