Question:
If $A=\left\{(x, y): y=e^{x}, x \in R\right\}$ and $B=\left\{(x, y): y=e^{-x}, x \in R\right\}$, then write $A \cap B$.
Solution:
We have:
$A=\left\{(0,1),(1, e),\left(2, e^{2}\right),\left(3, e^{3}\right), \ldots\right\}$
$B=\left\{(0,1),\left(1, e^{-1}\right),\left(2, e^{-2}\right),\left(3, e^{-3}\right), \ldots\right\}$
Thus, we get:
$\mathrm{A} \cap \mathrm{B}=\{(0,1)\}$