In the first two you should consider:
.
Let be denoted as the power set of and,
Let be denoted as the symmetric diference of the sets and and,
Let be denoted as the # of elements in set S.
Then, given and ,
a.) Determine the largest value possible of
b.) Determine the smallest value possible of
c.) Determine the largest value possible of
d.) Determine the smallest value possible of
(a) The symmetric difference between two sets is largest when both sets are disjoint. Then . ( indicates disjoint union.)
(b) The symmetric difference between two sets is when one set is a subset of the other. Here A can’t be a subset of B as A has more elements than B; so B must be a subset of A. Then . ( indicates subset exclusion.)
(c) If , then their power sets have nothing in common other than the empty set. In this case, .
(d) If , then every subset of B is also a subset of A. In this case, .