Problems 1-2
There two problems are making sure you have a understanding of three essential terms.

Problems 3-6
Go ahead and try to be creative in making up an example. Answers like { } for Problem 3 or {1, 2} for Problem 4 are not sufficient. We are looking for a real world example of sets with the indicated cardinality.

Problems 7-8
There two problems are distinguishing two essential sets; make sure you know the difference between the universal set and the empty set.

Problems 9-10
There two problems are making sure you have a understanding of two essential terms. What is needed here are real world examples.

Problems 11-18
A set is well-defined if there is no doubt as to what is included in the set and what is not.

Problems 19-26
See Example 1.

Problems 27-34
See Example 2.

Problems 35-42
The notation in these problems is called set-builder notation and you will find a description of this notation immediately following Example 2.

Problems 43-44
See Example 5 for part a, and Example 4 for part b. For part c, remember that sets are equal if they are the same set.

Problems 45-48
See Example 6.

Problem 49
A set is well-defined if there is no doubt as to what is included in the set and what is not.

Problems 50-51
Start with 1/2, then move to the thirds: 1/3, 2/3. Next, do the fourths (that have not previously been listed), then move to the fifths. Continue in this fashion for all the fractions.

Problems 52-53
The Problem of the Day relates sets to an everyday setting.

Note: Homework Hints are given only for the levels 1 and 2 problems. You can also check some sources for homework help on the Internet (see Links, below), or you can call the author at (707) 829-0606 or send an e-mail to: smithkjs@mathnature.com