Solution
= Solution
\b[True.] Boundedness follows from $\|x+y\|\le\|x\|+\|y\|$. To prove closedness of the <Minkowski sum>, let $z_j=x_j+y_j\in X+Y$ converge to $z$. By the <Bolzano-Weierstrass theorem>, the bounded sequence $x_j$ has a subsequence converging to $x$. Closedness gives $x\in X$. Along that subsequence, $y_j=z_j-x_j\to z-x$, which belongs to $Y$ by closedness. Thus $z=x+(z-x)\in X+Y$. This proves that the sum is bounded and closed.