Question

Let S be the set of all functions from the set A to the set A. If n(1) = k, then n(S) is

• A. k!
• B. k^k
• C. 2^k – 1
• D. 2^k

Answer 1

Answer: (B)

k^k

Answer 2

Each element of the set A can be given the image in the set A in k ways.

So, the required number of functions, i.e., n(S) = k× k × . . .(k times) = k^k