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

\[\text{Number of binary operations on a set with 2 elements} = 2^{2^2} \] 
\[ = 2^4 \] 
\[ = 16\]