question_answer

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

A) \[A\cap B=\phi \]                            

B) \[A\cap B\ne \phi \]

C) \[A\cup B={{R}^{2}}\]   

D)         None of these

Correct Answer: B

Solution :

Given sets are                 \[A=\{(x,\,\,y)y={{e}^{x}},\,\,x\in R\}\]and                 \[B=\{(x,\,\,y):y={{e}^{-x}},\,\,x\in R\}\] It is clear from the graph that two curves intersect at one point. \[\therefore \]  \[A\cap B\ne \phi \]