Let `S={a ,\ b ,\ c}` . Find the total number of binary operations on `Sdot`

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=3`,
`impliesn^(n^n) =3^(3^3)`

`impliesn^(n^n) =3^9`

Therefore, the total number of binary operations possible on set S is `3^9`