**Problem 1** can be phrased in your own words, but it would be a good idea to remember De Morgan’s laws.

**Problem 2** does not have a right or wrong answer, but it should outline the the steps shown in Example 3.

**Problems 3-10**

Draw a rectangle to represent the universe along with three interlocking sets, as shown in Example 3. Next, take care about the order of operations:

**Problems 3 and 4**: parentheses first

**Problems 5 and 6**: complement first

**Problems 7 and 8**: parentheses first, then complement

**Problem 9**: parentheses first; then intersection; finally complement

**Problem 10**: parentheses first; that is, complement of *B*, then complement of *C*; next intersection. Finish up with the complement of *A*, and finally the union.

**Problems 11-18**

These problems are designed to help you with terminology. Look at the terminology illustrated in Example 1.

**Problems 19-22**

See Example 1; watch the order of operations:

Problem 19: complement of *A* first; then *B*; finally union.

Problem 20: *A* first; then complement of *B*; finally intersection.

Problem 21: *A* intersect *B* first; then complement.

Problem 22: *A* union *B* first; then complement.

**Problems 23-34**

See Example 3; watch the order of operations.

**Problems 35-38**

Draw a rectangle for the universe, and then draw overlapping circles for the given sets. Label the universe and each circle.

**Problems 39-44**

Study each Venn diagram; how many sets? What is the final region? Hypothesize the relationship, and then check by carrying out the operations as shown in Example 3.[/tiippy]

**Problems 45-50**

Draw a Venn diagram for the left side of the equality. Then, draw a Venn diagram for the right side of the equality. If the final shaded answers for the two Venn diagrams are the same, then you have proved the result. If they are not the same, then you have disproved the result. See Examples 2 and 4.

**Problems 51-54**

These are survey problems with three sets, like Example 5. Draw three overlapping circles and label each circle.

Step 1: fill in the number of elements in the innermost set.

Step 2: fill in numbers in the other overlapping sections.

Step 3: fill in the other regions.

Step 4: Fill in the number outside the three circles and answer the questions asked in the problem.

**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/

**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/