Number of binary operations on the set a, b are: - Vidyadip

MCQ

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

A
$10$
✓
$16$
C
$20$
D
$8.$

✓

Answer

Correct option: B.

$16$

A binary operation $^*$ on $\{a, b\}$ is a function from $\{a, b\} \times \{a, b\} \rightarrow \{a, b\}$
i.e., $^*$ is a function from $\{(a, a), (a, b), (b, a), (b, b)\}.$
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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