Let $S_{1}, S_{2}$ and $S_{3}$ be three sets defined as
$\mathrm{S}_{1}=\{\mathrm{z} \in \mathbb{C}:|\mathrm{z}-1| \leq \sqrt{2}\}$
$\mathrm{S}_{2}=\{\mathrm{z} \in \mathbb{C}: \operatorname{Re}((1-\mathrm{i}) \mathrm{z}) \geq 1\}$
$\mathrm{S}_{3}=\{\mathrm{z} \in \mathbb{C}: \operatorname{Im}(\mathrm{z}) \leq 1\}$
Then the set $S_{1} \cap S_{2} \cap S_{3}$
Correct Option: , 3
For $|z-1| \leq \sqrt{2}, z$ lies on and inside the circle of radius $\sqrt{2}$ units and centre $(1,0)$.
For $\mathrm{S}_{2}$ Let $z=x+$ iy Now, $(1-i)(z)=(1-i)(x+i y)$
$\operatorname{Re}((1-i) z)=x+y$
$\Rightarrow x+y \geq 1$
$\Rightarrow S_{1} \cap S_{2} \cap S_{3}$ has infinity many elements
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