Question

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

• A. $B\subset A$
• B. $A\subset B$
• C. $A\cap B=\varphi$
• D. $A\cup B=A$

Answer 1

The correct option is C $A\cap B=\varphi$

$A=(x,y)$ are points on the curve $y=e^x$
$B=(x,y)$ are points on the line $y=x$
It can be observed from figure that both the curves have no point of intersection for all $x\in R$
Therefore, $A\cap B=\varphi$
Hence, option 'C' is correct.