Set theory counterexample

Question

Hello everyone, can someone please help me with the set theory question

(AB)C =A(BC)

I did a Venn diagram and I see that they’re not the same and now I need to do a proof by counter example. Any ideas where and how would do I start and do a set up for that?

Thank you

In: 2

Answer 1

Let x be in A and C, but not in B.

Then x is not in (AB)C because x is in C.

But x is in A, and not in B. Thus x is in A(BC).