Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
1  
Did you mean "without using the $\cup$ symbol"? –  Trevor Wilson Sep 20 '12 at 4:38
    
Yes, I can't use the U symbol to negate it. –  William 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. –  Trevor Wilson 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 –  Trevor Wilson 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. –  William Sep 20 '12 at 4:42

1 Answer 1

up vote 0 down vote accepted

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".

share|improve this answer
1  
Thanks. Got it. –  William Sep 20 '12 at 4:45
    
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.) –  Trevor Wilson Sep 20 '12 at 4:46

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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