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Prove absorption law

  1. Sep 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove the absorption law A U (A and B) = A

    2. Relevant equations

    3. The attempt at a solution

    I need to prove the sets are equal.

    I don't know how to prove the right hand as a subset of the left hand.
    For left hand as subset of right hand, it's pretty simple (we can define a new called G holding x in A and in B), and G is subset of A, then G U A is A (definition of subset and Union).

    But how do I prove the right hand?
    I started writing "There exists a set A...." and I thought about using partition, but then I couldn't go on anymore. If I say there exists an arbitrary set B, and x in A and B, then I am again writing the first proof.

    Can someone please help me? Thanks.
     
  2. jcsd
  3. Sep 15, 2011 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    Is this set theory or Boolean Algebra? Boolean Algebra I think.
     
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