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Question
Number of binary operations on the set {a, b} are
(A) 10
(B) 16
(C) 20
(D) 8
Solution
A binary operation * on {a, b} is a function from {a, b} × {a, b} → {a, b} i.e., * is a function from {(a, a), (a, b), (b, a), (b, b)} → {a, b}.
Hence, the total number of binary operations on the set {a, b} is 24 i.e., 16.
The correct answer is B.
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