Question

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

• A. $B\subseteq A$
• B. $A\subseteq B$
• C. $A\cap B=\varnothing$
• D. $A\cup B=R$

Answer 1

The correct option is C

$A\cap B=\varnothing$

Finding the relation between set $A$and $B$:

Given, $A=\left\{(x,y):y=e^x,x\in R\right\}$ and $B=\left\{\right(x,y):y=x,x\in R\}$.

$A=(x,y)$ are points on the curve $y=e^x$.
$B=(x,y)$ are points on the line $y=x$.

We'll see this by drawing a graph:

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, the correct answer is an option (C).