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.
- A.
xy
- B.
2(x+y)
- C.
yx
- 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.