Question

If sets $A$ and $B$ are defined as
$A=\left\{\right(x,y)|y=\frac{1}{x},x\ne 0,x\in R\},$
$B=\left\{\right(x,y)|y=-x,x\in R\},$ then

• A. $A\cap B=A$
• B. $A\cup B=B$
• C. $A\cap B=\varphi$
• D. $A\cup B=A$

Answer 1

The correct option is C

$A\cap B=\varphi$

$x\in (A\cap B)\Rightarrow x\in A\text{and}x\in Bi.e.y=\frac{1}{x}\text{and}y=-x$

$\therefore x\in A\cap B\Rightarrow -x=\frac{1}{x}$
$\Rightarrow -x^2=1$
$\Rightarrow x^2=-1,$
This is not possible for any real value of $x$.
$\therefore A\cap B=\varphi$