Symmetry difference between a and a =(a-a)∩(b-a)= empty set ∪ empty set = empty set.
That is to say, when any set A is symmetrically differentiated from itself, it is equal to an empty set. If a is not equal to an empty set, then the symmetry difference between a and a is equal to an empty set. Of course, the symmetry difference between A and A is not equal to A. ..
An operation *, if the operation between x and itself is equal to itself, that is, x*x=x, it is said to satisfy the idempotent law. Obviously, the symmetric difference operation does not satisfy the idempotent law, because it is not aimed at any element X, and there is X * X = X