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Logical Definition of Two Disjoint Sets

  1. Jul 6, 2011 #1
    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 [itex] A \cap B = \emptyset [/itex] 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:

    [itex] \forall x (x\in A \rightarrow x \notin B) [/itex]

    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
  2. jcsd
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