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Q.
The number of binary operations on the set $\{a, b\}$ are
Relations and Functions - Part 2
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 .