Mathematics - Sets and Relations Question with Solution | TestHub

Let $S=\mathbf{N}\cup \{0\}$. Define a relation $R$ from $S$ to $\mathbf{R}$ by :
$\mathrm{R}=\left\{(x,y):{\log }_{\mathrm{e}}y=x{\log }_{\mathrm{e}}\left(\frac{2}{5}\right),x\in \mathrm{S},y\in \mathbf{R}\right\}$

Then, the sum of all the elements in the range of $R$ is equal to :