If $A,B$ sets, what does $A \Delta B$ mean?

Question

If $A,B$ sets, what does $A \Delta B$ mean?

I am doing exercises in measure theory, sigma algebras, where in one exercise I shall prove that $A \Delta B$ lies in the sigma algebra. But I have never seen this notation before, what does it mean?

Answer 1

Generally $$A\Delta B=(A-B)\cup(B-A)$$ This is called the symmetric difference; it is all elements that are in one set or the other, but not both.

Answer 2

It means, by definition:

$$A \Delta B=(A \setminus B) \cup ( B \setminus A).$$