Question

Find the total number of binary operations on {a, b}.

Answer 1

Number of binary operations on a set with n elements is $n^{n^2}$.

Here, S = {a, b}
Number of elements in S = 2
$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{binary}\mathrm{operations}\mathrm{on}\mathrm{a}\mathrm{set}\mathrm{with}2\mathrm{elements}=2^{2^2} \\ =2^4 \\ =16 \end{gathered}$$