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Math Help - [SOLVED] Proofs

  1. #1
    akeem
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    [SOLVED] Proofs

    Prove the following:

    1. For all set A and B, A c A U B

    2. For all sets A and B, A U B c A ∩ B

    3. For all set A and B, A - B = A ∩ B

    4. For all sets A and B, if A c B, then B c A

    5. For all sets A, B, and C, A-(B U C) = (A - B) ∩ (A - C)
    Last edited by akeem; November 22nd 2007 at 08:43 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by akeem View Post
    Prove the following:

    1. For all set A and B, A c A U B
    For all x in A x is of necessity in (A union B), by definition of union.

    You may worry that this does not work if A is the null set, but as the
    null set is a subset of every set the result still holds (and you don't really
    need to so worry).

    RonL
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  3. #3
    Super Member

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    Hello, akeem!

    Are there typos?
    . . Most of these are not true . . .


    Prove the following for all sets A,\,B,\,C:

    1.\;\;A \:\subseteq \:A \cup B . True

    2.\;\;A \cup B \;\subseteq \; A \cap B . Not true

    3.\;\;A - B \:= \:A \cap B . Not true

    4.\;\;\text{If }A \subseteq B,\text{ then }B \subseteq A . Not true

    5.\;\;A - (B \cup C) \:= \:(A - B) \cap(A - C) . True

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