Question:
Number of binary operations on the set {a, b} 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.