Question

If \[A = \left\{ \left( x, y \right) : y = e^x , x \in R \right\} and B = \left\{ \left( x, y \right) : y = e^{- x} , x \in R \right\}\]write\[A \cap B\] 

Answer 1

We have:
A =\[\left\{ \left( 0, 1 \right), \left( 1, e \right), \left( 2, e^2 \right), \left( 3, e^3 \right), . . . \right\}\]

B =\[\left\{ \left( 0, 1 \right), \left( 1, e^{- 1} \right), \left( 2, e^{- 2} \right), \left( 3, e^{- 3} \right), . . . \right\}\] 

Thus, we get:
AThus, we get:
A\[\cap\]B =\[\left\{ \left( 0, 1 \right) \right\}\]