Is anything wrong about this method of getting the elements of a set, that are in no other set?

I have sets A, B, C, D, E, and I'm trying to get the elements of set A that are not in any other set.

If Q is the union of B, C, D, and E.

And Z is the intersection of A, and Q.

What I want would be the symmetric difference between A, and Z?


closed as unclear what you're asking by Henno Brandsma, max_zorn, José Carlos Santos, Namaste, ArsenBerk Nov 2 '18 at 9:59

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  • $\begingroup$ No, you'd want $A \backslash Q$. What's the purpose of $Z$? $\endgroup$ – Sambo Nov 1 '18 at 23:25
  • $\begingroup$ @Sambo - Whoops, that was supposed to be "difference between A and Z", but I guess that's the wrong method anyway? ... Correcting question... $\endgroup$ – Malady Nov 2 '18 at 0:33

What you describe -- $A\triangle (A\cap Q)$ -- will give the right result, but is is simpler just to write $A\setminus Q$.

If you have a particular reason to prefer avoiding the $\setminus$ operation, it is fine to do what you do. Just make sure your reader(s) can see what this reason is, or the apparently convoluted procedure will probably confuse them a lot.


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