Set Identities

Commutativity

We know that the union and intersection operations are commutative. We also know that the set difference operation is not commutative. There’s a difference between keeping the elements of $A$ that are not in $B$ and keeping the elements of $B$ that are not in $A$. Both sets can have elements that are not common. Therefore, we can say that ${A\setminus B} \ne {B\setminus A}$. But if we look at the symmetric difference, we can see that it’s commutative. This is because the union operation is commutative, as exhibited below: