Decide whether the following propositions are true or false. If the claim is valid, supply a short proof, and if the claim is false, provide a counterexample. Using Heine-Borel Theoren (a) An arbitrary intersection of compact sets is compact. (b) Let A CR be arbitrary, and let KCR be compact. Then An K is also compact. ... (c) If Fi 2 F22 F32 F4 2 is a decreasing sequence of nonempty closed sets, then the intersection EN Fn +0. (d) A finite set is always compact. (e) A countable set is always compact.