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)

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?