# Expression for this set?

I've got the set builder notation of a set:

{x|x is an element of at most one of the three sets A, B, and C}

And I must determine an expression for it using:

$\bigcup$, $\bigcap$, $-(substraction)$, $'(complement)$

What i have so far is:

$A \bigcap B' \bigcap C' \bigcup B \bigcap A' \bigcap C' \bigcup C \bigcap A' \bigcap B'$.

x is either in A and NOT B and NOT C or B and NOT A and NOT C or C and NOT B and NOT A

Which would be equivalent to:

$A - B - C \bigcup B - A - C \bigcup C - A - B$

Are my current paths correct?

• Are you referring to the case where X is not in any set? So $(A' \bigcap B' \bigcap C')$? – pstatix Jan 21 '18 at 1:02
• How would you express it using the $-(substitution)$? Just $A'-B'-C'$? – pstatix Jan 21 '18 at 1:06