Question

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

• A. 10
• B. 16
• C. 20
• D. 8

Answer 1

The Correct Option is B

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).