For this problem, you may want to review set theory from CSE 20, especially the size of power set of a set. (6 points) Let n be a positive integer and define [n] to be the set of the first n positive integers. That is, n] 1,2,3,.. .,n]. We want to select two disjoint subsets A, B of [n]. In how many ways can we do this? Optional.) Now we want to select three subsets A, B, C of [n] such that AC C, B C C, and AnB-. In how many ways can we do this?

Runners run around the school's football field. the cross country coach determines that the width of the field is seventy yards shorter than the length. part a write an expression that represents the perimeter of the football field. let x represent the length of the football field. include parentheses in your expression. next, write an equivalent expression that does not include parentheses. what property or properties did you use to simplify? explain. part b the cross country coach later determines that the length of the football field is 120 yards. all students must run five laps. using your answer from part a, determine the actual number of yards that each athlete must run in the tryouts. in order to make the team, students must complete the laps in 6 minutes. how quickly must they run each lap?