Question

Let $A=\{(x,y):y=e^x,x\in R\}$
$B=\{(x,y):y=e^{-x},x\in R\}$. Then

• A. $A\cap B=\varphi$
• B. $A\cap B\ne \varphi$
• C. $A\cup B=R^2$
• D. $noneofthese$

Answer 1

The correct option is B $A\cap B\ne \varphi$

Ans. $\left(b\right)$.
$y=e^x,y=e^{-x},$ meet where $e^x=e^{-x}$ or $e^{2x}=1$
$\therefore x=0$ and hence $y=1$. These curve meet at $(0,1)$ so that $A\cap B=(0,1)$.
In other words $A\cap B\ne \varphi$.