If A = {1, 2, 3, ..., 10}. B = {m/n, m, n ∈ A and m < n and gcd of (m,n) = 1} Then number of elements in set B is

Question

If \(A=\{1,2,3, \ldots ., 10\}. \) B = {\(\frac{m}{n}, m, n \in\) A and m < n and gcd of (m, n = 1)}. Then number of elements in set B is

(1) 30

(2) 31

(3) 28

(4) 29

Answer 1

Correct option is (2) 31

\(n=1 \ m \in \phi\)   ... 0  

\(n=2 m=1 \Rightarrow \frac{m}{n}\text{ can be }\frac{1}{2} \ldots 1\)   

\(n=3 m=1,2 \Rightarrow \frac{m}{n} \text{can be} \frac{1}{3}, \frac{2}{3} \ldots 2\)