Given nonempty subsets A and B of positive real numbers, define A) Show that sup(A B) = (sup A)(sup B).

B) Show that

C) Show that, if A and B are bounded subsets of real numbers, then sup (A - B) = max {(sup A)(sup B), (sup A)(inf B), (inf A)(sup B), (inf A)(inf B)}.

D) Give an example of two nonempty bounded sets A and B for which sup(A B) (sup A)(sup B)

The marked price of an article is 25% above its selling price and the cost price is 30% less than its marked price . find the discount percent and gain percent. only a brainlest can solve it i will mark you brainlest

Suppose you just purchased a digital music player and have put 8 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 8 songs is played once in random order. find the probability that among the first two songs played (a) you like both of them. would this be unusual? (b) you like neither of them. (c) you like exactly one of them. (d) redo () if a song can be replayed before all 8 songs are played.

Assume that y varies inversely with x. if y=1.6 when x=0.5 find x when y=3.2 acellus answer