Question:
If $A=\left\{(x, y): y=\frac{1}{x}, 0 \neq x \in R\right\}$ and $B=\{(x, y): y=-x, x \in R\}$, then write $A \cap B$.
Solution:
We have:
$A=\left\{(x, y): y=\frac{1}{x}, 0 \neq x \in R\right\}$
$=\left\{(1,1),\left(2, \frac{1}{2}\right),\left(3, \frac{1}{3}\right),\left(4, \frac{1}{4}\right), \ldots\right\}$
And,
$B=\{(x, y): y=-x, x \in R\}$
$=\{(1,-1),(2,-2),(3,-3),(4,-4), \ldots\}$
Thus, we get:
$A \cap B=\emptyset$