Relation between XOR and Symmetric difference I noticed that XOR and symmetric difference use the same symbol, $\oplus$.  
They also seem to have a similar structure:
XOR: $(Q \wedge \neg P)\vee(P\wedge \neg Q)$
Symmetric Difference: $(A\cap B^C)\cup(B\cap A^C)$
Is there a relation between them?

Yes, there is. Let $A\;\triangle\; B$ denote the symmetric difference of the sets $A$ and $B$. Given an object $x$, 
$$x\in A\;\triangle\; B\iff (x\in A)\text{ XOR }(x\in B).$$
In general, one has a correspondence between statements in set theory and statements in logic, e.g.
$$x\in A\cup B\iff (x\in A)\text{ OR }(x\in B)$$
$$x\in A\cap B\iff (x\in A)\text{ AND }(x\in B)$$
$$x\in A^c\iff\text{NOT }(x\in A)$$
So, for example, $A\setminus B=A\cap B^c$, so 
$$x\in A\setminus B\iff x\in A\cap B^c\iff(x\in A)\text{ AND }(x\in B^c)\iff (x\in A)\text{ AND }(\text{NOT }(x\in B))$$
