# Thread: Clarification on some set notation

1. ## Clarification on some set notation

I have a homework problem that reads as (A symmetric difference B) with a line over the top. (This is just part of the problem - I'm trying to be sure I'm not asking for the answer, just clarifying the bits I don't understand.) Does that mean the complement of the symmetric difference as a whole? Symmetric difference in a Venn diagram of just (A symmetric difference B) would be the two non-intersecting bits of A and B highlighted and nothing else (not the overlap or the rest of the stuff in the universe) in my understanding (correct me, please, if that is wrong.)

I'm thinking, if that's right, that the complement of (A symmetric difference B) is then everything outside of the two sets A and B... but I'm not sure about the overlap part -- I think that it isn't included, but I'm not complete certain.

Thanks!

2. ## Re: Clarification on some set notation

Yes it means complement of symmetric difference. The complement of symmetric difference is $(U - A \cup B) \cup ( A \cap B)$ Everything outside and the intersection of A and B.