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Number of binary operations on the set {...

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

A

10

B

16

C

20

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
A binary operation * on {a,b} is a function from `{a,b}xx{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.
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