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Math Help - Algebraic laws to simplify

  1. #1
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    Algebraic laws to simplify

    For any sets A and B, use algebraic laws of sets to simplify
    (a) [ A - (A-B)] - B
    (b) A - [ B - (A-B)]
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  2. #2
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    Re: Algebraic laws to simplify

    Use X \setminus Y = X \cap Y^c to convert the set minus into intersection/union of sets
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  3. #3
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    Re: Algebraic laws to simplify

    Quote Originally Posted by Bingk View Post
    Use X \setminus Y = X \cap Y^c to convert the set minus into intersection/union of sets
    How to put the set minus into the set?
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  4. #4
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    Re: Algebraic laws to simplify

    I don't understand your question ...

    Example:
    X \setminus ( Y\setminus Z) = X \ ( Y \cap Z^c) = X \cap (Y \cap Z^c)^c = X \cap (Y^c \cup Z) = \\ (X \cap Y^c) \cup (X \cap Z)

    The last line is from distribution (you can check Algebra of sets - Wikipedia, the free encyclopedia for more "shortcuts")
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