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Math Help - Set Theory

  1. #1
    Super Member Deadstar's Avatar
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    Set Theory

    Let X and Y be finite non-empty sets. Write down a formula for the number of different functions from X to Y.

    Ans: #Y^#X. (hash symbol doesn't seem to work in latex..?)

    Can anyone explain why this is?
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  2. #2
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    If n is the number of elements in X and m is the number of elements in Y for each x \in X we have m choices in Y for its image in a mapping. Therefore we have m^n possible mappings.
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  3. #3
    Super Member Deadstar's Avatar
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    I need an example to picture this. What are the 8 possible mappings then in X has 3 elements and Y has 2?
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  4. #4
    MHF Contributor
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    Suppose X = {a, b, c} and Y = {d, e}.

    1. f: X->Y

    f(a) = d
    f(b) = d
    f(c) = d

    2. f: X->Y

    f(a) = d
    f(b) = d
    f(c) = e

    3. f: X->Y

    f(a) = d
    f(b) = e
    f(c) = d

    4. f: X->Y

    f(a) = e
    f(b) = d
    f(c) = d

    5. f: X->Y

    f(a) = e
    f(b) = e
    f(c) = d

    6. f: X->Y

    f(a) = e
    f(b) = d
    f(c) = e

    7. f: X->Y

    f(a) = d
    f(b) = e
    f(c) = e

    8. f: X->Y

    f(a) = e
    f(b) = e
    f(c) = e
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