If sets A and B are defined as $\mathrm{A}=\left\{(\mathrm{x},\mathrm{y}):\mathrm{y}={\mathrm{e}}^{\mathrm{x}},\mathrm{x}\in \mathrm{R}\right\},\mathrm{B}=\left\{\right(\mathrm{x},\mathrm{y}):y=\mathrm{x},\mathrm{x}\in \mathrm{R}\}$, then 

$$\begin{gathered} \mathrm{A}=(\mathrm{x},\mathrm{y})\text{ are points on the curve }\mathrm{y}={\mathrm{e}}^{\mathrm{x}} \\ \mathrm{B}=(\mathrm{x},\mathrm{y})\text{ are points on the line }\mathrm{y}=\mathrm{x} \\ \text{ It can be observed from figure that both the curves have} \\ \text{no point of intersection for all }\mathrm{x}\in \mathrm{R} \end{gathered}$$

The graph of $\mathrm{y}={\mathrm{e}}^{\mathrm{x}},\mathrm{y}=\mathrm{x}$ do not intersect $\Rightarrow \mathrm{A}\cap \mathrm{B}=\mathrm{\varnothing }$