Mathematics - Sets and Relations Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{A}=\{1,2,\dots ,10\}\\ & \mathrm{B}\left\{\frac{\mathrm{m}}{\mathrm{n}}=\mathrm{m},\mathrm{n}\in \mathrm{A},\mathrm{m}<\mathrm{n},\gcd (\mathrm{m},\mathrm{n})=1\right\}\\ & \mathrm{n}(\mathrm{B})\end{array}$


$\mathrm{n}=2\left\{\frac{1}{2}\right\}$
$\mathrm{n}=3\left\{\frac{1}{3},\frac{2}{3}\right\}$

$\begin{array}{ll}\mathrm{n}=4& \left\{\frac{1}{4},\frac{3}{4}\right\}\\ \mathrm{n}=5& \left\{\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5}\right\}\end{array}$

$\begin{array}{ll}\mathrm{n}=6& \left\{\frac{1}{6},\frac{5}{6}\right\}\\ \mathrm{n}=7& \left\{\frac{1}{7},\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7}\right\}\\ \mathrm{n}=8& \left\{\frac{1}{8},\frac{3}{8},\frac{5}{8},\frac{7}{8}\right\}\end{array}$

$\begin{array}{ll}\mathrm{n}=9& \left\{\frac{1}{9},\frac{2}{9},\frac{4}{9},\frac{5}{9},\frac{7}{9},\frac{8}{9}\right\}\\ \mathrm{n}=10& \left\{\frac{1}{10},\frac{3}{10},\frac{7}{10},\frac{9}{10}\right\}\\ \mathrm{n}(\mathrm{B})=31& \end{array}$