# Negation of $x∈A\cup B$ without using $\cup$

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?

• Did you mean "without using the $\cup$ symbol"? Sep 20 '12 at 4:38
• Yes, I can't use the U symbol to negate it. Sep 20 '12 at 4:39
• 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. Sep 20 '12 at 4:41
• 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 Sep 20 '12 at 4:41
• 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. 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".