Question

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

• A. $A\subseteq B$
• B. $B\subseteq A$
• C. $A\cap B=\varphi$
• D. $A\cap B\ne \varphi$

Answer 1

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

$A$ is the set of all points on the graph of $y=e^x$. $B$ is the set of all points on the line $y=x$. Since the curves are non-intersecting, we have $A\cap B=\varphi$.