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

• A

  $A \cap B=\phi$
• Correct answer
  B

  $A \cap B \neq \phi$
• C

  $A \cup B=R^2$
• D

  None of these

Solution

Given sets are $\begin{aligned} & A=\left\{(x, y): y=e^x, x \in R\right\} \text { and } \\ & B=\left\{(x, y): y=e^{-x}, x \in R\right\}\end{aligned}$

It is clear from the graph that two curves intersect at one point. $\therefore \quad A \cap B \neq \phi$

Hence, the correct answer is option: 'B'.