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Please check this problem

  1. Sep 5, 2007 #1
    1. The problem statement, all variables and given/known data

    I am to prove that AU(AΠB)=AΠ(AUB)=A where Π means intersection

    2. Relevant equations

    3. The attempt at a solution

    LHS xЄA or, xЄ(AΠB)
    => xЄA or, (xЄA and xЄB)
    => (xЄA or, xЄA) and (xЄA or,xЄB)
    =>xЄA and xЄ(AUB).............................This is precisely AΠ(AUB)

    x is an element of both A and (AUB),that is what the and operation mean.
    Hence xЄA..........................proved from one side.

    Now we are to prove that yЄA =>yЄ AU(AΠB)
    Since A is a subset of AU(AΠB),it follows that if yЄA,it must be true that yЄ AU(AΠB)
    Again,since AU(AΠB)=AΠ(AUB),hence yЄ AΠ(AUB) too.

    Hence proved.
    Last edited: Sep 5, 2007
  2. jcsd
  3. Sep 5, 2007 #2


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    Science Advisor
    Homework Helper

    You certainly have the idea. This stuff is all relatively obvious, so how much you have to show depends a bit on your class.
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