Let A be a nonempty bounded subset of R and put m = inf A. For a fixed k R. with k > 0, define the set B = kA = {ka: a A}. (1) Show that km is a lower bound of the set B 2 Say briefly why it follows from the statement in question (1) that inf B km 3 Show that inf B km. (Hint: you may show first that ( inf B) is a lower bound of the set A).: (4) Conclude that inf (kA) = k inf (A)