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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