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Math Help - Set Operations

  1. #1
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    Set Operations

    Hi All, hope I have the correct forum first of all.

    I have the following set expression:

    (Y \cap X) \cap (X \cap Y)

    I want to simplify the expression further. However I need to show full workings out. Could I simply just use the idempotence operation so it would become the following?

    Y \cap X
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  2. #2
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    Re: Set Operations

    Quote Originally Posted by richtea9 View Post
    I have the following set expression:
    (Y \cap X) \cap (X \cap Y)
    Y \cap X
    Well for all sets A we have A\cap A=A.
    Also (Y\cap X)=(X\cap Y).
    What more do you need?
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  3. #3
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    Re: Set Operations

    Quote Originally Posted by Plato View Post
    Well for all sets A we have A\cap A=A.
    Also (Y\cap X)=(X\cap Y).
    What more do you need?
    So the correct operation is idempotence? I wouldn't first have to use distributivity or commutativity?

    Just to note: I have simplified this expression from another one.
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  4. #4
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    Re: Set Operations

    Quote Originally Posted by richtea9 View Post
    So the correct operation is idempotence? I wouldn't first have to use distributivity or commutativity? Just to note: I have simplified this expression from another one.
    I think only your instructor can comment of the level of rigor required of you.
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  5. #5
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    Re: Set Operations

    "Idempotence" is not an operation- it is a property.

    What definition of A\cap B are you using that A\cap B= B \cap A isn't immediate?
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