Each of the $m$ elements of $A$ independently receives one of $n$ images in $B$. The <multiplication principle> therefore gives \b[$n^m$ 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.

Solution

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

 Solution (source code)