Question

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

• A. \( A \cap B = \emptyset \)
• B. \( A \cap B \neq \emptyset \)
• C. \( A \cup B = \mathbb{R}^2 \)
• D. None of these

Hint:

To find the intersection of sets defined by functions, equate the functions and solve for the common values of \( x \) and \( y \).

Answer 1

The Correct Option is B