**[tippy title=”Problems 1-4″]Problems 1-4**

There are many problems throughout the text labeled IN YOUR OWN WORDS. Just relax; do not be afraid to give your opinion. For the most part, these questions do not have “right” or “wrong” answers. Several of these problems ask for examples. Do your best to find examples that are your own. You should spend about five minutes in answering each of these questions. [/tippy]

**[tippy title=”Problems 5-8″]Problems 5-8**

A set is well defined if there is no disagreement about whether a particular element is or is not in a given set. See Example 1.[/tippy]

**[tippy title=”Problems 9-14″]Problems 9-14**

To designate a set by roster means to list the elements in a set (see Example 1). Don’t forget that each elements should be listed only once. For example, in Problem 9a, do not list the letters *m*, *a*, or *t* more than once.[/tippy]

**[tippy title=”Problems 15-20″]Problems 15-20**

You need to think of a word description for each of these sets. See Example 2.[/tippy]

**[tippy title=”Problems 21-26″]Problems 21-26**

These problems are designed to give you practice with set-builder notation. First, write down how you might pronounce the statement, and then list the elements in the set using the roster method, as shown in Example 1.[/tippy]

**[tippy title=”Problems 27-35″]Problems 27-35**

These problems are designed to help you compare and contrast the description, roster, and set-builder notations for sets.[/tippy]

**[tippy title=”Problems 36-39″]Problems 36-39**

Remember that the empty set is a subset of every set and that any set is a subset of itself.

In **Problem 36 and 37,** work systematically, as shown in Examples 8 and 9.

In **Problem 38 and 39**, use the results of Problems 36 and 37 to work systematically using patterns.[/tippy]

**[tippy title=”Problems 40-43″]Problems 40-43**

Remember that one set divides the universe into two parts.

In** Problem 40,** the set of people who are 30 and under is the set, and the set of people who are over 30 is the complement. Divide the universe into two parts. Then, draw the set of drivers as a circle overlapping both parts.

In **Problem 41**, the set of people who are males, and the set of people who are females is the complement. Divide the universe into two parts. Then, draw the set of bike riders as a circle overlapping both parts.

In **Problem 42,** the universe is the set of automobiles.

In **Problem 43**, the universe is the set of communication devices.[/tippy]

**[tippy title=”Problems 44-45″]Problems 44-45**

These two problems require that you understand that cardinality is the number of elements in a set, that sets are equivalent if they have the same number of elements, and are equal if they are the same set. See Examples 4 and 5.[/tippy]

**[tippy title=”Problems 46-54″]Problems 46-54**

For these problems you need to distinguish among the symbols for element, subset, and proper subset. See Example 7. [/tippy]

**Note:** Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section). As a last resort, you can call the author at (707) 829-0606.

On the other hand, the problems designated “Problem Solving” generally require techniques that do not have textbook examples.

There are many sources for homework help on the internet.

**Algebra.help**

Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.

http://www.algebrahelp.com/

**Ask Dr. Math**

Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.

http://mathforum.org/dr.math/

**Quick Math**

This site provides online graphing calculators. This is especially useful if you do not have your own calculator.

http://www.quickmath.com/

**The Math Forum @ Drexel**

This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.

http://mathforum.org/