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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

Answers (1)
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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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