Intersection of affine halfspaces is convex

Question

Given any finite amount of affine halfspaces, $H_1,\ldots,H_n \subset\mathbb{R^d}$, are their intersection, $\bigcap_{i=1}^{n}H_i$, necessarily closed and convex?

Answer 1

Yes, because the intersection of finitely many closed subsets is closed and the intersection of any family of convex sets is convex.