Question

If $A$ and $B$ are two sets defined as $A=\left\{\right(x,y):x=yx,y\in R\}$ and $B=\left\{\right(x,y):x=y+1x,y\in R\}$ , then

• A. $A\cap B=A$
• B. $A\cap B=B$
• C. $A\cap B=\varphi$
• D. None of the above

Answer 1

The correct option is C $A\cap B=\varphi$

Set $A$ represents all points lying on the line $y=x$ and set $B$ represents all the points on the line $x=y+1$
Slope of both the lines are same so the lines are parallel.
So they have no point in common.
$\Rightarrow A\cap B=\varphi$
So option $C$ is correct.