Question

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

• A. 10
• B. 16
• C. 20
• D. 8

Answer 1

Answer: (B)

16

Answer 2

A binary operation * on {a, b} is a function from {a, b} × {a, b} $\to$ {a, b}
i.e., * is a function from {(a, a), (a, b), (b, a), (b, b)} $\to$ {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 (16).