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Suppose that A is a finite set with 3 elements, B is a finite set with 8 elements, and C is a finite set with 2 elements. How many functions are there from the set A x B to the set C?

So I have tried this: Number of elements in

AxB = |AxB| = |A|*|B| = 24

Number of elements in C = |C| = 2

So I thought number of functions from AxB to C:

f: AxB -> C = |C|^|AXB| = 2^24 = 16777216

But 16777216 is not the correct answer. What am I doing wrong here?

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    You are doing nothing wrong unless if you are neglecting to mention additional constraints in the problem. The answer to the currently written problem is indeed $2^{24}$ – 2017-02-21
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    The question is literally what is posted on top. There is nothing more to it. And that is why I am so confused too. – 2017-02-21
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    @script_before_java: What is the claimed correct answer? – 2017-02-21
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    It won't show me until Friday. I guess I will have to go and talk to the instructor. Thanks for your time guys. – 2017-02-21
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    Every function is between two (possibly indistinct) sets. Considering the identity functions, there are at least proper class many functions. Each function is a set so there are precisely proper-class many functions. – 2017-02-22
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    I breifly considered that maybe to book is claiming a function from A to B need not map all elements of A. E.g. f (x)=$\sqrt {x} $ is a real valued function that does't map from all reals. But that is so very incorrect i have a hard time imagining a text making such a claim. But if so the answer would be $3^24$ as each element is map to one ore another or not mapped at all. But that is really very wrong as in no accurate way can we say that function maps "from" A if it isn't actually defined for all A. – 2017-02-22
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    Perhaps, the question is meant as "how many SURJECTIVE functions are there from $A\times B$ to $C$ ?". In this case, the answer would be $2^{24}-2$ – 2017-02-22

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