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The number of commutative binary operation on the set A = {1, 2} is ___________.
Question

The number of commutative binary operation on the set A = {1, 2} is ___________.

A.

32

B.

8

C.

16

D.

64

Correct option is B

The number of commutative binary operations on a set with n elements is given by the formula:n(n+1)2Given the set A={1,2}, which has 2 elements:Number of commutative binary operations on the set A=2(2+1)2=23=8\text{The number of commutative binary operations on a set with } n \text{ elements is given by the formula:}\\\frac{n(n+1)}{2}\\\text{Given the set } A = \{1, 2\}, \text{ which has 2 elements:}\\\text{Number of commutative binary operations on the set } A = \frac{2(2+1)}{2} = 2^3 = 8​​

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