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Math Help - Proof-injection,bijection

  1. #1
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    Proof-injection,bijection

    f: X--->Y and g: Y----> Z are functions. Prove that

    a) if both f and g are injective then g*f is injective

    b) if both f and g are surjective then g*f is surjective

    c) if both g*f is a bijection, then f is an injection and g is a surjection

    ( * is that small circle that means one function 'plugged into' into another)
    Last edited by topsquark; January 18th 2008 at 06:14 AM. Reason: Restored question
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by anncar View Post
    f: X--->Y and g: Y----> Z are functions. Prove that

    a) if both f and g are injective then g*f is injective

    b) if both f and g are surjective then g*f is surjective

    c) if both g*f is a bijection, then f is an injection and g is a surjection

    ( * is that small circle that means one function 'plugged into' into another)
    similar problems were dealt with here. see if it helps. if it doesn't come back. i hope you know the defintions of injective, surjective and bijective before even thinking about proceeding with these questions. the first 2 or 3 posts and the last post is relevant. in the middle, there's a lot of philosophical stuff
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