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

Explanation

We have given set `S = a,b,c`, we need to find the total number of binary operations possible for the set ‘S’.

We know that the total number of binary operations on a set ‘S’ with ‘n’ elements is given by `n^(n^n)`

Here `n=2`,
`impliesn^(n^n) =2^(2^2)`

`impliesn^(n^n) =2^4=16`

Therefore, the total number of binary operations possible on set S is `2^4=16`