Let A be a finite set having x elements and let B be a finite set having y…

2014

Let A be a finite set having x elements and let B be a finite set having y elements. What is the number of distinct functions mapping B into A.

  1. A.

    xy

  2. B.

    2(x+y)

  3. C.

    yx

  4. D.

    y! / (y-x)!

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Correct answer: A

To find the number of distinct functions mapping set B into set A, recall that a function assigns each element in the domain to exactly one element in the codomain. Here, set B is the domain with y elements and set A is the codomain with x elements. For each of the y elements in B, there are x possible choices in A to map to. Multiplying these independent choices gives x multiplied by itself y times, which equals x raised to the power of y. Thus, the number of distinct functions is x^y.

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