Let \(A={1,2,3,\ldots \ldots .,10}\) and \(B={\frac{m}{n}:m,n\in A,m Then \(n(B)\) is equal to

\(\text{for}m=1\Rightarrow \frac{1}{2},\frac{1}{3},\frac{1}{4},\ldots \ldots \ldots \frac{1}{10}\to 9\\ \text{for}m=2\Rightarrow \frac{2}{3},\frac{2}{5},\frac{2}{7},\frac{2}{9}\to 4\\ \text{for}m=3\Rightarrow \frac{3}{4},\frac{3}{5},\frac{3}{7},\frac{3}{8},\frac{3}{10}\to 5\\ \text{for}m=4\Rightarrow \frac{4}{5},\frac{4}{7},\frac{4}{9}\to 3\\ \text{for}m=5\Rightarrow \frac{5}{6},\frac{5}{7},\frac{5}{8},\frac{5}{9},\to 4\\ \text{for}m=6\Rightarrow \frac{6}{7}\to 1\\ \text{for}m=7\Rightarrow \frac{7}{8},\frac{7}{9},\frac{7}{10},\to 3\\ \text{for}m=8\Rightarrow \frac{8}{9}\to 1\\ \text{for}m=9\Rightarrow \frac{9}{10}\to 1\\ \text{then}n(B)=31\)