Proving Symmetric Difference of A and B Let A and B be sets. Define the symmetric difference of A and B as A∆B= (A ∪ B) − (A ∩ B).
(a) Prove that A∆B = (A − B) ∪ (B − A)
I tried to start this but am getting really lost. if someone could try to help that would be great 

Using that $A - B = A \cap B^C$:
$A \Delta B = $
$(A \cup B) - (A \cap B) = $
$(A \cup B) \cap (A \cap B)^C =$
$ (A \cup B) \cap (A^C \cup B^C) =$
$ (A \cap (A^C \cup B^C)) \cup  (B \cap (A^C \cup B^C)) = $
$(A \cap B^C) \cup  (B \cap A^C) = $
$(A - B) \cup (B - A)$
