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

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?

• – Mauro ALLEGRANZA Dec 19 '16 at 12:35
• As a note, you should use \triangle for symmetric difference, i.e. $A\triangle B$ rather than $A\Delta B$. In the latter case it looks like either $\Delta$ or $\Delta B$ is a variable. – G. H. Faust Dec 19 '16 at 14:42

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