Question

Number of binary operations on the set {a,b} are
(a)10
(b)16
(c)20
(d)8

Answer 1

A binary operation $\ast$ on {a,b}is a function from {a,b} $\times$ {a,b}$\to$ {a,b}
i.e., $\ast$ is a function from $\left\{\right(a,a),(a,b),(b,a),(b,b\left)\right\}\to a,b.$
Hence, the total number of binary operations on the set {a,b} is $2^4$ i.e., 16.
Thus, the correct answer is (b).