1. The problem statement, all variables and given/known data 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. a) An arbitrary intersection of compact sets is compact. b)A countable set is always compact. 3. The attempt at a solution a) If I took an infinite amount of intersections of closed intervals of the real line, I could get a set that is not bounded, And by the Heine-Borel theorem a set is compact if and only if it is closed and bounded. b) The set of naturals is countable but not bounded so again by the Heine-Borel theorem this is not true.