# Verifying an identity

1. Aug 27, 2011

### autre

I need to verify this identity:

(A\B)$\Delta$C = (A$\Delta$C)$\Delta$(A$\bigcap$B)

(with delta standing for the symmetric difference, I don't know the proper latex code)

I've tried it "brute force" several times, working out each side and simplifying it until the sides are equal (it's likely that I'm messing up a negation somewhere) and I've found this method rather cumbersome. Is there any simpler way to solve this?

2. Aug 27, 2011

### I like Serena

Hi autre!

Have you tried drawing a so called Venn diagram?

3. Aug 27, 2011

### mathman

I used Venn diagrams and got the result you are looking for. There are 7 disjoint sets involved. Is that the brute force you tried?

4. Aug 27, 2011

### autre

That's it, mathman. Thanks guys.