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Question
The number of commutative binary operations that can be defined on a set of 2 elements is ____________ .
Options
8
6
4
2
Solution
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 = \[2^\frac{2\left( 2 - 1 \right)}{2} \]
\[ = 2^1 \]
\[ = 2\]
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