MCQ
The number of commutative binary operation that can be defined on a set of $2$ elements is:
- A$8$
- B$6$
- C$4$
- ✓$2$
✓
Answer
Correct option: D.
$2$
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 $=2\frac{2(2-1)}{2}=2^1$
$=2$
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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