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Math Help - set algebra

  1. #1
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    set algebra

    using set algebra laws prove the following:


    1) (A-B) U (B-A) = (A U B) - (A ∩ B)


    2) ((A ∩ B)' U B)' = 0
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  2. #2
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    Re: set algebra

    Start by replacing X - Y by X ∩ Y', then use De Morgan's laws and distributivity of ∩ over U.
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  3. #3
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    Re: set algebra

    Hello, beast!

    Here is the second one.
    I'll let you supply the reasons.


    [2]\;\;\big[(A \cap B)' \cup B\big]' \:=\:\emptyset

    \big[(A \cap B)' \cup B\big]'

    . . =\;\big[(A' \cup B') \cup B\big]'

    . . =\;\big[A' \cup (B' \cup B)\big]'

    . . =\; \big[A' \cup U\big]'

    . . =\;U'

    . . =\; \emptyset
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  4. #4
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    Re: set algebra

    1st line - deMorgans?
    2nd line - complement law?
    3rd line - ???
    4th line - ???


    please help
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