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

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Question

(C) binary operation $^*$ on a set $S$ is a function from $S 	imes S$ to $S$.Here,the set is $S = \{a, b\}$,so $S 	imes S = \{(a, a), (a, b), (b, a)

Vedclass · Accepted Answer

$16$

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(C) binary operation $^*$ on a set $S$ is a function from $S 	imes S$ to $S$.Here,the set is $S = \{a, b\}$,so $S 	imes S = \{(a, a), (a, b), (b, a), (b, b)\}$.The number of elements in $S 	imes S$ is $n(S 	imes S) = 2 	imes 2 = 4$.The number of elements in the codomain $S$ is $n(S) = 2$.The total number of functions from $S 	imes S$ to $S$ is given by $(n(S))^{n(S 	imes S)} = 2^4$.Calculating this,we get $2^4 = 16$.Thus,the total number of binary operations on the set $\{a, b\}$ is $16$.The correct answer is $C$.

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

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