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Math Help - Help!: Consider two functions f: X ->Y and g: Y->X where X and Y are two finite sets.

  1. #1
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    Question Help!: Consider two functions f: X ->Y and g: Y->X where X and Y are two finite sets.

    I need some help with these questions from my textbook that I know these questions will be on an upcoming quiz and I am having difficulty with.

    Consider two functions f: X ->Y and g: Y->X where X and Y are two finite sets.

    g○f = 1x

    Argue by either providing a detailed proof or counter example.

    a) Does necessarily f○g = 1y?
    b) Is f, g necessarily one-one?
    c) Is f, g necessarily onto?
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  2. #2
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    Can someone help me out here?
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