The number of commutative binary operation that can be defined on… - Vidyadip

Question

The number of commutative binary operation that can be defined on a set of 2 elements is:

8
6
4
2

✓

Answer

2

Solution:
The number of commutative binary operations on a set of n elements is $\text{n}\frac{\text{n}(\text{n}-1)}{2}$.
Therefore,
Number of commutative binary operations an a set of 2 elements $=2\frac{2(2-1)}{2}=2^1$
$=2$

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