Task 1. Given are the sets $A=\{1,2, x, 5,9\}, B=\{2, y, 3\}$. Determine the numbers $x$ and $y$ such that the set $B$ has three elements and $B \subseteq A$.
Solution. Since $3 \in B$ and $B \subseteq A$, we conclude that $3 \in A$, so it must be that $x=3$. Now, since set $B$ must have three elements, it holds that $y \neq 2$ and $y \neq 3$. Furthermore, from $B \subseteq A$, it follows that $y \in \{1,5,9\}$.