Homework Help: Logical Definition of Two Disjoint Sets

1. Jul 6, 2011

MushroomPirat

1. The problem statement, all variables and given/known data

I'm self-studying Daniel Velleman's How to Prove It, and I'm wondering if there is some way to write that "Sets A and B are disjoint" using symbols, other than the $A \cap B = \emptyset$ given in the book.

2. Relevant equations

3. The attempt at a solution

I'm thinking that if A and B are disjoint, then for every element x, where if x is an element of A, then x is not an element of B. Or:

$\forall x (x\in A \rightarrow x \notin B)$

Thanks !

Edit: Right after I posted this, I realized I could just prove the equivalency, and it turned out to be a pretty trivial proof (if I did it right). So, I think this thread can be deleted now.

Last edited: Jul 6, 2011