Question:
Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C) 20 (D ) 8
Answer:
Let S is a finite set containing n elements.
Since binary operation on S is a function from S*S to S, therefore total number of binary operations on S is the
total number of functions from S*S to S = (nn)2
Given Set = {a,b}
Total number of elements = 2
Total number of binary operations = (22)2 = 24 = 16
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