Question

The number of commutative binary operations that can be defined on a set of 2 elements is ____________ .

Options

• 8

• 6

• 4

• 2

Answer 1

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 = \[2^\frac{2\left( 2 - 1 \right)}{2} \]
                           \[ = 2^1 \]
                           \[ = 2\]