Question

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

• A. $A \cap B = \phi$
• B. $A \cap B \neq \phi$
• C. $A \cup B = R ^ { 2 }$
• D. None of these

Answer 1

Answer: (B)

$A \cap B \neq \phi$

Answer 2

$\because y = e ^ { x } , y = e ^ { - x }$will meet, when $e ^ { x } = e ^ { - x }$

⇒ $e ^ { 2 x } = 1 , \therefore x = 0 , y = 1$

∴ A and B meet on (0, 1), ∴ $A \cap B = \phi$.