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# Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C) 20 (D ) 8

Q. 19 Number of binary operations on the set $\{a, b\}$ are
(A) 10
(B) 16
(C) 20
(D ) 8

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Binary operations on the set $\{a, b\}$ are is a function from  $\{a, b\}\times \{a, b\}\rightarrow \{a, b\}$

i.e. * is a function from   $\left \{ (a,b),(b,a),(a,a),(b,b) \right \} \rightarrow \{a, b\}$

Hence, the total number of binary operations on set  $\{a, b\}$ is $2^{4}=16.$

Hence, option B is correct.

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