Number of binary operations on the set {a, b} are

Question:

Number of binary operations on the set {ab} are

(A) 10

(B) 16

(C) 20

(D) 8

Solution:

A binary operation * on $\{a, b\}$ is a function from $\{a, b\} \times\{a, b\} \rightarrow\{a, b\}$

i.e., ${ }^{*}$ is a function from $\{(a, a),(a, b),(b, a),(b, b)\} \rightarrow\{a, b\}$.

Hence, the total number of binary operations on the set $\{a, b\}$ is $2^{4}$ i.e., 16 .

The correct answer is B.

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