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Math Help - Simplifying Sets using Properties

  1. #1
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    Simplifying Sets using Properties

    First of all, n = intersection because the actual symbol would work for me

    Code:
    (A U B U C U D) n (A U B U C) n (A U B) n C
    I need to simplify the set expression given above. I think the answer is (A U B) n C? Maybe even A n C?

    Maybe the above is correct but I want to know how to show the stages of simplifying it. For example, by commutativity, associativity and idempotence.

    Any help would be great, thanks.
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  2. #2
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    Re: Simplifying Sets using Properties

    Quote Originally Posted by richtea9 View Post
    First of all, n = intersection because the actual symbol would work for me
    Code:
    (A U B U C U D) n (A U B U C) n (A U B) n C
    I need to simplify the set expression given above. I think the answer is (A U B) n C? Maybe even A n C?
    This is always true: (X\cup Y)\cap X=X.
    So (A\cup B\cup C)\cap (A\cup B)=(A\cup B).
    Can you finish?

    BTW: Simple LaTeX code,
    [TEX](A\cup B\cup C)\cap (A\cup B)[/TEX]
    gives (A\cup B\cup C)\cap (A\cup B)
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  3. #3
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    Re: Simplifying Sets using Properties

    Quote Originally Posted by Plato View Post
    This is always true: (X\cup Y)\cap X=X.
    So (A\cup B\cup C)\cap (A\cup B)=(A\cup B).
    Can you finish?

    BTW: Simple LaTeX code,
    [TEX](A\cup B\cup C)\cap (A\cup B)[/TEX]
    gives (A\cup B\cup C)\cap (A\cup B)
    Hi

    Thanks for the reply, am I right by thinking its just A? (Looking at the first expression you gave.) If so I don't see how this would show the same as the set expression I gave on a venn diagram.
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  4. #4
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    Re: Simplifying Sets using Properties

    Quote Originally Posted by richtea9 View Post
    am I right by thinking its just A? (Looking at the first expression you gave.) If so I don't see how this would show the same as the set expression I gave on a venn diagram.
    The answer is (A\cup B)\cap C.
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