(a) subset, P, of the powerset 24, such that Given a set of animals, A = {dog, cat, rat, mouse}, write down the largest P = {P; € 2^|{cat, mouse} Z P;} (b) List the elements of the power set of A that are excluded from P.

Determine whether the set S={1,x2,2+x2} spans P2.

Suppose a set A has 2,048 subsets. How many distinct objects are contained in A?

The number of 5-element subsets from a set containing n elements is equal to the number of 6-element subsets from the same set. What is the value of n? (Hint: the order in which the elements for the subsets are chosen is not important.)