Question

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

Answer 1

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 \(n^{n^2}\). 

Here n = 3,

⇒ \(n^{n^2} = 3^{3^2}\)

⇒ \(n^{n^2} = 3^9\)

∴ The total number of binary operations possible on set ‘S’ is 3⁹.