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Question

Let S be the set of all functions from the set A to the set A. If $$n(A) = k$$ then $$n(S)$$ is


A
k
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B
kk
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C
2k1
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D
2k
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Solution

The correct option is C $$\displaystyle k^k$$
Given, $$n(A) =k$$

defining a function implies that every element in A is mapped to exactly one element in A

so, every element in A has k choices to make in the range set A.
likewise, there are k elements in A

$$\therefore $$ number of functions that can be defined =$$k\times k\times k\times k\times$$ ..... (k times)

i.e. $${ k }^{ k }$$

Mathematics

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