I have been asked to prove that: $(A \cup B)$ \ $(A \cap B) = (A$ \ $B) \cup (B$ \ $A)$
I have got this far in the proof:
$(A \cup B)$ \ $(A \cap B)$
$(x \in (A \cup B)) \land (x \not \in (A \cap B))$ - definition of set difference
$(x \in A \lor x \in B) \land (x \notin A \land x \notin B)$ - definition of set union and set intersection
I can't see how to go any further, as using the distributive laws may get quite complicated considering there are 2 things either side of the conjunctive operator. Is this the right direction to head or have I started off on the wrong foot?