Suppose there are 3 sets: A, B, and C s.t. (U for 'union')(adsbygoogle = window.adsbygoogle || []).push({});

(A - B) U (A - C) U (B - C)

Now, I was wondering if there is the precedence of parentheses over set operations (union in this case).

This is saying "every element in A but not in B" or "every element in A but not in C" or "every element in B but not in C".

I know that nothing in C is contained in this union and that everything in A is minus those that are in both A and B and both A and C. Now, the last difference, B - C, annoys me. Would B - C override A - B and include every element in B but not in C (and not those in both A and B)?

Would this be a case of symmetric difference? For example

(A - B) U (B - A)

would this include everything but the intersection (if A and B are not disjoint or empty and A does not equal B)

(sidenote: Has there been a problem with Latex, it wouldn't show this tag:

[tex]\left(A\setminus B\right)\cup \left(A\setminus C\right)\cup \left(B\setminus C\right)[/tex (last bracket intentionally left out so it would show text))

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Set operation problem

**Physics Forums | Science Articles, Homework Help, Discussion**