A <binary relation> on $A$ is any <subset> of the <Cartesian product> $A\times A$. There are $n^2$ ordered pairs, and each can independently be included or omitted. Hence \b[the number of <binary relations> is $2^{n^2}$]. This also gives one relation when $n=0$, namely the <empty set>.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 1 / b / ii / Solution

 Solution (source code)