Question

If $A=\left\{\left(x,y\right):y=\frac{1}{x},0\ne x\in R\right\}$ and $B=\left\{\left(x,y\right):y=-x,x\in R\right\}$, then write $A\cap B$.

Answer 1

We have:
$A=\left\{\left(x,y\right):y=\frac{1}{x},0\ne x\in R\right\}$
= {$\left(1,1\right),\left(2,\frac{1}{2}\right),\left(3,\frac{1}{3}\right),\left(4,\frac{1}{4}\right)$, ...}
And,
$B=\left\{\left(x,y\right):y=-x,x\in R\right\}$
= $\left\{\left(1,-1\right),\left(2,-2\right),\left(3,-3\right),\left(4,-4\right),...\right\}$
Thus, we get:
$A\cap B$ = $\varnothing$