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:

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

To me this reads as:

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?


That's good but you are missing one case. "At most one" means...

  • $\begingroup$ Can you elaborate? What case am I missing? $\endgroup$ – pstatix Jan 21 '18 at 1:01
  • 1
    $\begingroup$ Are you referring to the case where X is not in any set? So $(A' \bigcap B' \bigcap C')$? $\endgroup$ – pstatix Jan 21 '18 at 1:02
  • $\begingroup$ At most one means possibly none! $\endgroup$ – Arnaud Mortier Jan 21 '18 at 1:02
  • $\begingroup$ Yes :) we posted simultaneously. $\endgroup$ – Arnaud Mortier Jan 21 '18 at 1:03
  • $\begingroup$ How would you express it using the $-(substitution)$? Just $A'-B'-C'$? $\endgroup$ – pstatix Jan 21 '18 at 1:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.