Question

The number of elements in the set $A\cap B\cap C$ is

• A. $0$
• B. $1$
• C. $2$
• D. $\infty$

Answer 1

The correct option is B $1$

$A=$ Set of points on and above the line $y=1$ in the Argand plane.
$B=$ Set of points on the circle $(x-2{)}^2+(y-1{)}^2=3^2$
$C=Re(1-i)z=Re\left(\right(1-i\left)\right(x+iy)$
$\Rightarrow x+y=\sqrt{2}$
Hence ($A\cap B\cap C$) $=$ has only one point of intersection.