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Math Help - Basic Set theory question

  1. #1
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    Basic Set theory question

    Hi,

    I am having trouble with this one, please help if you can.

    Let f:X ->Y be a function, Let A and B be subsets of X and let C and D be subsets of Y.

    Prove that

    f-1(C U D) = f-1(C) U f-1(D).

    f-1(x) means the inverse function of some element x.

    I know I need to start by saying,

    Let x /in f-1(C U D)

    and I think this means that there is some y /in f(C U D) such that f-1(y) = x.

    But I am not sure on how to proceed. Any help is appreciated.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Smancer View Post
    Hi,

    I am having trouble with this one, please help if you can.

    Let f:X ->Y be a function, Let A and B be subsets of X and let C and D be subsets of Y.

    Prove that

    f-1(C U D) = f-1(C) U f-1(D).

    f-1(x) means the inverse function of some element x.

    I know I need to start by saying,

    Let x /in f-1(C U D)

    and I think this means that there is some y /in f(C U D) such that f-1(y) = x.

    But I am not sure on how to proceed. Any help is appreciated.
    so you have to prove f^{-1}(C \cup D) \subseteq f^{-1}(C) \cup f^{-1}(D) and f^{-1}(C) \cup f^{-1}(D) \subseteq f^{-1}(C \cup D)

    to start you off on the first one, let x \in f^{-1}(C \cup D). then then there is some y \in (C \cup D) such that f^{-1}(y) = x. But y \in (C \cup D) means y \in C or y \in D. thus.....?
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