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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?

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

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  • $\begingroup$ Can you elaborate? What case am I missing? $\endgroup$ – pstatix Jan 21 '18 at 1:01
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    $\begingroup$ 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

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