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)

Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu . assume that the population has a normal distribution. a laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with sequals 17.6 milligrams. a confidence interval of 173.8 mgless than muless than 196.2 mg is constructed for the true mean cholesterol content of all such eggs. it was assumed that the population has a normal distribution. what confidence level does this interval represent?