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Math Help - Set Theory Q

  1. #1
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    Set Theory Q

    Hi I need help with the following:

    1.
    For any sets A and B, prove that:
    a) A = (A ∩ B) or (A\B)
    b) (A\B) or (B\A) = (A or B)\(A∩B)

    2. For any sets A,B,C, prove that if
    A\(B or C) = (A\B)or(A\C), then A∩(B or C) ⊆ A∩B∩C

    3. For any sets A and B, prove that A\(A\B) = A∩B

    4. Prove that if A\(B\C) ⊆ (A\B)\C then A∩C = 0


    Any or all would be much appreciated!
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  2. #2
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    Re: Set Theory Q

    anyone?
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  3. #3
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    Re: Set Theory Q

    Quote Originally Posted by DirectorRico View Post
    For any sets A and B, prove that:
    a) A = (A ∩ B) or (A\B)
    b) (A\B) or (B\A) = (A or B)\(A∩B)
    2. For any sets A,B,C, prove that if
    A\(B or C) = (A\B)or(A\C), then A∩(B or C) ⊆ A∩B∩C
    3. For any sets A and B, prove that A\(A\B) = A∩B
    4. Prove that if A\(B\C) ⊆ (A\B)\C then A∩C = 0

    DO NOT BUMP.

    You first question is meaningless.

    (A\setminus B)\cup(B\setminus A)=(A\cap B^c)\cup(B\cap A^c) EXPAND.

    A\setminus(B\setminus C)=(A\cap (B\setminus C)^c=A\cap (B^c\cup C)

    AND (A\setminus B)\setminus C=(A\cap B^c)\cap C^c
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  4. #4
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    Re: Set Theory Q

    My mistake.

    Could you possibly answer #2,#3 or #4?
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  5. #5
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    Re: Set Theory Q

    Quote Originally Posted by DirectorRico View Post
    Could you possibly answer #2,#3 or #4?

    I did answer each of those.
    You have to do the work.

    Remember: This is not a homework service.

    We help. You do the work.
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