Construct the negation of each statement below without using the following symbols: ∩, ∪, ⊆, ⊇, ⊂, ⊃, \, △, and =.

I know that the negation is simply $x∉A\cup B$, but how do I represent that without using the ∉ symbol? Thanks!

Could I say x ∈ ~A $\land$ ~B ?

Can I even use the and symbol $\land$ on sets?

  • 1
    $\begingroup$ Did you mean "without using the $\cup$ symbol"? $\endgroup$ Sep 20 '12 at 4:38
  • $\begingroup$ Yes, I can't use the U symbol to negate it. $\endgroup$
    – William
    Sep 20 '12 at 4:39
  • $\begingroup$ I'm not sure what your last comment means. The $\notin$ symbol is not on your list in the first paragraph of things you can't use. $\endgroup$ Sep 20 '12 at 4:41
  • $\begingroup$ Does $\wedge$ mean "and"? If so, you can't use it on sets, but you can use it on sentences, and that might give a clue as to how to solve the problem $\endgroup$ Sep 20 '12 at 4:41
  • $\begingroup$ Sorry for not being clear. I can't use the union symbol ∪. I CAN use the ∉ symbol. So I can't negate it by saying x∉A∪B because that uses the ∪ symbol. $\endgroup$
    – William
    Sep 20 '12 at 4:42

Hint: $x \in A \cap B$ if and only if $x \in A$ and $x \in B$. You can say a similar thing for $\cup$ and "or".

  • $\begingroup$ You're welcome. Don't forget to accept the best answer by clicking the check mark next to it on the left (feel free to wait for more answers if you like.) $\endgroup$ Sep 20 '12 at 4:46

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