Question

Number of binary operations on the set {a, b} are

(A) 10

(B) 16

(C) 20

(D) 8

Answer 1

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.