This is from "How to Prove It", by Velleman.The problem is asking me to prove that (AΔC)Δ(B\A) = (A∪B)ΔC I expanded (AΔC)Δ(B\A) = [((AvC)^(A^C))v(B\A)]^[((AvC)^(A^C))^(B\A)].After simplifying this answer, I should simply get (A∪B)ΔC = ((AvB)vC)^((AvB)^C). But I've attempted this many times, and did not reach this conclusion. Any help would be appreciated.. thanks.

*I know the proper form is x ∈ A∪B = (x ∈ A) v (x ∈ B), but I'm just writing A v B for short. Also, this is what I tried (sorry for the bad handwriting):