Add additional or convert existing problems to "prove/disprove"

[dcernst]

See comments from Reviewer 5.

[dcernst]

One example from Reviewer 5: Theorem 3.26/Problem 3.27: This is entirely personal preference, but perhaps an interesting suggestion to consider. How about make these two one problem – ask students to explore the relationship between P(S)∪P(T) and P(S∪T ), determine the relationship, and prove that they are precisely correct? Exploration is part of the goal here, and this is a fun problem for exploring and building a better understanding of power sets.

[dcernst]

Reviewer 5: Definition 3.39/Exercise 3.40/Exercise 3.41: Again, personal preference. Students benefit from playing around with infinite indexing sets. How about encourage that in Exercises 3.40 and 3.41? Possibly in the context of R, such as “provide an example of ...” with multiple parts, including

• a collection of three sets such that the collection is not pairwise disjoint, the union equals R, and the intersection of the collection equals ∅;
• a collection of infinitely many sets such that the collection is not pairwise disjoint, the union equals R, and the intersection of the collection equals ∅; and
• a collection of infinitely many sets such that the collection is pairwise disjoint, the union equals R, and the intersection of the collection equals ∅.

[dcernst]

Done.