 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/1/e/i/solution

Each of the

m

elements of

A

independently receives one of

n

B

. The multiplication principle therefore gives $n^{m}$ functions. In particular an empty set domain has exactly one function to any

B

, so here

0^{0}

is interpreted as

1

; a nonempty domain has no function to an empty set codomain.

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