# Set theory proof

## Main Question or Discussion Point

Hi, I have been trying for a very long time to prove the following set theory identity

(A union B) intersect (B union C) intersect (C union A) = (A intersect B) union (B intersect C) union (C intersect A).

I thought that I could simplify (A U B) intersect (B U C) intersect (C U A)
as [B U (A intersect C) ]intersect (C U A), but venn diagrams show that this is not correct.

Thanks

Related Set Theory, Logic, Probability, Statistics News on Phys.org
haruspex
Homework Helper
Gold Member
Do you know how to distribute union over intersection and vice versa?
(AuB)^(BuC) = (A^(BuC))u(B^(BuC))
Since B^(BuC) = B you can simplify that a little.
Just keep applying those rules and the result should drop out.
If you get stuck, post your working so far.

Thank you, it worked. I probably did it in a more convoluted manner than required, but I was able to do it in around 12 lines.

I didn't realise that you could distribute like that at first.