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Help, proving set theorem

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove A contained B iff A n B = A

    2. Relevant equations

    none

    3. The attempt at a solution

    I tried to do the questions but im just not sure if i did it right. id appreciate if you can check my work and let me know what changes i have to make. thanks

    the symbol "n" means "intersect"
    U for Union


    (=>) Assume A contained B

    Let x is an element of A, since A n A = A, x is an element of A and x is an element of B

    Case 1: x is an element of A: Since A contained B, x is an element of B so
    x is an element of A n B

    Case 2: x is an element of B: If x is an element of B then
    x is an element of (A n B)

    Hence x is an element of A n B

    This shows A contained A n B

    (<=) Assume A n B = A then

    A’=A’UA
    = A’ U (A n B)
    =(A’UA) n (A’U B)
    = empty set n A’ U B
    = A’ U B

    Hence
    Universe = A’ U B
     
  2. jcsd
  3. Nov 29, 2008 #2
    You don't need the "since A n A = A" part.

    You don't need cases here. You want to show that A n B = A: Do this by first showing that A n B is a subset of A and then showing that A is a subset of A n B. (Do you see why this implies A n B = A?)

    What is A' exactly? Also, you state that A’=A’UA but then you have that A’=A’UA is the empty set. Surely there is something wrong here. You just need to show that A is a subset of B. Do this by picking a random member of A and show that it also belongs to B.
     
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