How can I express the non-intersecting sections of multiple sets with a single set operation? I don't have a lot of experience with set theory, as I suspect this question will make clear!
As the title says, I'm interested in expressing the non-intersecting sections of three sets using a single set operation.
What I mean is, how would you express the gray shaded regions in the following Venn Diagram?

My best guess is that this has to do with complements... something like 

((A ∪ B) ∪ (A ∪ C) ∪ (B ∪ C))C

...maybe? But I am concerned that this complement would also include the universe, U, which I don't want to be part of the selection. I also suspect that my notation is wrong, so apologies if that's the case.
Thanks for any help!
 A: $(A-B-C)\cup (B-A-C) \cup (C-A-B)$
Or you could do:
$(A \cup B \cup C) -(A \cap B)-(A \cap C)-(B \cap C)$
In either case, you want to use subtraction of sets. In case you are not familiar, here is an example:
Consider the set $D=\{1,2,3,4,5\}$ and $E=\{3,4,5,6,7\}$.
Then the set $(D-E)=\{1,2\}$ and the set $(E-D)=\{6,7\}$.
Hence, $(D-E)\cup (E-D)=\{1,2\} \cup \{6,7\} = \{1,2,6,7\}$.
A: Hint: The shaded $A$ region is $A \cap (B \cup C)^c$. 
A: I think ((A ∪ B) ∪ (A ∪ C) ∪ (B ∪ C))$^c$ would just give $(A \cup B \cup C)^c$
how about
$ (A \cap (B \cup C)^c) \cup (B \cap (A \cup C)^c) + (C \cap(A \cup B)^c)$ 
A: So you want the part $A$ without those parts in $B$ and $C$; hence you want $$A \backslash (B \cup C)$$
Likewise you want $B$ without either $A$ or $C$, hence you also-want $$B \backslash(A \cup C)$$; and similarly you want $C$ without $A$ or $B$; hence also desire $$C \backslash(A \cup B)$$
Now overall you want any of the above, hence, you union to obtain
$$\boxed{A \backslash (B \cup C) \;\;\cup\;\; B \backslash(A \cup C)  \;\;\cup\;\; C \backslash(A \cup B)}$$
Hope that helps!

Note:: $X \backslash Y$ means the set $X$ without the elements in the set $Y$; read "X less Y".
