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Math Help - Number of functions from one set to another?

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    Number of functions from one set to another?

    How many functions, injections, surjections, bijections and relations from A to B are there, when A = {a, b, c}, B = {0, 1}?

    Edit: I know the answer should be 64, but I don't know how to arrive at that.
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  2. #2
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    Quote Originally Posted by posix_memalign View Post
    How many functions, injections, surjections, bijections and relations from A to B are there, when A = {a, b, c}, B = {0, 1}?
    Edit: I know the answer should be 64, but I don't know how to arrive at that.
    I have no idea what you mean by 64.
    There are 2^3 functions A\to B.
    There are no injections A\to B.
    Therefore, no bijections.
    There are 6 surjections.
    Because \|A\times B\|=6 there are 2^6 relations from A\to B is you allow the empty relation,
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    Quote Originally Posted by Plato View Post
    I have no idea what you mean by 64.
    There are 2^3 functions A\to B.
    There are no injections A\to B.
    Therefore, no bijections.
    There are 6 surjections.
    Because \|A\times B\|=6 there are 2^6 relations from A\to B is you allow the empty relation,
    Thanks, but why do you need the \|? Why isn't the cartesian product by itself sufficient?
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    Quote Originally Posted by posix_memalign View Post
    Thanks, but why do you need the \|? Why isn't the cartesian product by itself sufficient?
    #(X)= |X|= \|X\| these are all common symbols standing for the number of elements in a given set.
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