Show that the set $U$ contains the set $S$ I want to show that the set $U=\{\left(x, y\right)\in\mathbb R^2 \ | \ \left(x-1\right)^2 + \left(y-1\right)^2 <3\}$ contains the set $S=\{\left(x, y\right)\in\mathbb R^2 \ | \ x \geq1; \ y\geq0; \ x^2+y^2 \leq 4\}$
It is easy to see that $U$ contains $S$ graphically. But I don't know how to show it mathematically. If I can get a little hint, I will appreciate it.

$U$ and $S$ are connected (and convex) subsets of the plane. To prove that $S \subseteq U$ or $U \subseteq S$, you need to:

*

*Find one point, i.e. $(1,0)$, that belongs to both of $S$ and $U$.

*Prove that the boundary of $S$ doesn't intersect the boundary of $U$.

In addition, to prove specifically that $S \subseteq U$ you need to:


*Find one point of $U$ that does not belong to $S$.

