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

SOLUTION:

Alternative (B) is right. A = {a, b} and

A x A = {(a,a), (a,b),(b,b),(b,a)} Number of components = 4

Along these lines, number of subsets = 2^4 = 16.