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Math Help - True / False Sets

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    37

    True / False Sets

    TRUE or FALSE. Assume that the statement applies to all sets.



    a)
    A -(B -C) = (A -B) C
    FALSE

    b)
    (A -C) -(B -C) = A B
    TRUE

    c)
    A U (B C) = (A U B) (A U C)
    TRUE

    d)
    A (B U C) = (A U B) (A U C)
    FALSE

    e)
    (A U B) U A = A
    ????

    f)
    If A B = A U B, then A = B.
    ???


    Thanks
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  2. #2
    Banned
    Joined
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    Posts
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    Quote Originally Posted by captainjapan View Post
    TRUE or FALSE. Assume that the statement applies to all sets.



    a)
    A -(B -C) = (A -B) C
    FALSE

    b)
    (A -C) -(B -C) = A B
    TRUE

    c)
    A U (B C) = (A U B) (A U C)
    TRUE

    d)
    A (B U C) = (A U B) (A U C)
    FALSE

    e)
    (A U B) U A = A
    ????

    f)
    If A B = A U B, then A = B.
    ???


    Thanks

    f) IS true here is a proof:

    assume AUB = A \cap B.

    Assume xεA ====> xεA v xεΒ <====> xε(ΑUB) ====> xε(A \cap B) (Since AUB = A \cap B.) and xε(A \cap B)=====> xεA & xεB ====> xεB.

    Hence .... A is a subset of B .In the same way we prove B is a subset of A


    e) is also true here is a proof:


    (AUB')' U A' = (A' \cap B)UA' = (A' \cap T)U(A' \cap B) =


    A' \cap(TUB) = A' \cap T = A'

    SINCE :
    A' \cap T=A' and BUT=T WHERE T is for true
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