Question

The number of commutative binary operations that can be defined on a set of 2 elements is
(a) 8
(b) 6
(c) 4
(d) 2

Answer 1

(d) 2
The number of commutative binary operations on a set of n elements is $n^{\frac{n\left(n-1\right)}{2}}$.

Therefore,
Number of commutative binary operations on a set of 2 elements = $$\begin{gathered} 2^{\frac{2\left(2-1\right)}{2}} \\ =2^1 \\ =2 \end{gathered}$$