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Proof in Discrete math

  1. Sep 9, 2006 #1
    Hi, I would like some help for the following problems.

    please bear with me with my special notation:
    I- intersection
    U- union
    S- universal set
    ~- complement

    I need to prove that: let be A and B two sets. prove
    (A U B) I (A I (~B))=A

    what I did is:
    (A U B) I (A I (~B))

    =[(A I B) U A] I [(A I B) U ~B]/distribution

    =A I [(~B U A) I (~B U B)]

    =A I [(~B U A) U S)

    =A I (~B U A)

    =(A I (~B)) U (A I A)

    =AUA=A //i'm not sure here (A I (~B)) =A

    problem 2

    Can we conclude that A=B if A,B,C are sets such that
    i) A U C = B U C
    ii) A I C = B I C

    how can I treat this problem?

    Thank you for your help
  2. jcsd
  3. Sep 9, 2006 #2


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    As stated, that's not true. (e.g. let A be any nonempty set, and let B equal A)

    but that said...

    It doesn't look like you applied this rule right.

    This step is wrong too.

    I would try and draw a picture to help with my intuition.
  4. Sep 9, 2006 #3
    You should use Venn diagrams: http://en.wikipedia.org/wiki/Venn_diagram. By the way, why did you post this in the Calculus forum?
  5. Sep 9, 2006 #4


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    Because it's the Calculus & Beyond forum.
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