1. Let F := {1, 2, 4, 8}, let G := {1, 3, 9}, and let H := {0, 5, 6, 7}. Let U := {0, 1, 2, . . . , 9} be the universe. Which of the following pairs of sets are disjoint?   2. Let S and T be two sets,...

1. Let F := {1, 2, 4, 8}, let G := {1, 3, 9}, and let H := {0, 5, 6, 7}. Let U := {0, 1, 2, . . . , 9} be the universe. Which of the following pairs of sets are disjoint?

2. Let S and T be two sets, with n = |S| and m = |T|. For each of the following sets, state the smallest cardinality that the given set can have. Give examples of the minimum-sized sets for each part. (You should give a family of examples— that is, describe a smallest-possible set for any values of n and m.)

1. S ∪ T

2. S ∩ T

3. S – T