Let X be a set and let $P(X)$ denote the set of all subsets of X, that is $P(X)= \{A|A\subseteq X\}$. given $A,B\in P(X),$ define $A \triangle B:=(A\setminus B)\cup(B\setminus A)$.
Prove that $(P(X), \triangle)$ is a group.
Using the definition of a group I assume I have to show that there exist an associativity, identity, and inverse.
Yes, you are right. You have to show that this is an associative binary operation with identity and inverse. (It's also commutative).
From what I can tell, that was your question.
Hint.
First figure out the identity, then figure out the inverses.
Save associativity for last- it is just tedious definition chasing.