question_answer

If sets A and B are defined as \[A=\{(x,y):y={{e}^{x}},x\in R\}\]and \[B=\{(x,y):y=x,x\in R\}\]then

A) \[B\subset A\]

B)                         \[A\subset B\]

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

D)         \[A\cup B=A\]

Correct Answer: C

Solution :

Given that \[A=\{(x,y):y={{e}^{x}},x\in R\}\] and        \[B\{(x,y):y=x,x\in R\}\] It is clear from the figure that the two curves never intersect, it means there is no common point.                 i.e.,        \[A\cap B=\phi \]