#### 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 2^{4} i.e., 16.

The correct answer is B.

Is there an error in this question or solution?

Solution Number of Binary Operations on the Set {A, B} Are Concept: Concept of Binary Operations.