Problems 1-2

There are many problems throughout the text labeled IN YOUR OWN WORDS.
Problem 3

Remember intersection is “and”, union is “or,” and complement is “not.”
Problem 4

You should remember both of these formulas.
Problem 5

Remember the conditions under which this is true.
Problem 6 Try to find a counter-example.
Problems 7 and 8; 9 and 10

Contrast union, intersection, and complement for the given sets.
Problems 11-12

These are complements; to find the complement of a set, look at the universe

(set U), and list all elements in the universe that are not in the given set. Notice that Problems 11 and 17 are the same, and so are Problems 12 and 18.
Problems 13-16

For multiples of three, “count by 3”; {3, 6, 9, … }

For multiples of five, “count by 5”; {5, 10, 15, … }
Problems 17-18

These are complements; to find the complement of a set, look at the universe

(set U), and list all elements in the universe that are not in the given set. Notice that Problems 11 and 17 are the same, and so are Problems 12 and 18.
Problems 19-24

These problems deal with unions, intersections, and complements.
Problems 19, 21a, 23b, and 24a

These are unions; to find the union of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in either of the given sets. Remember, the empty set is { }.
Problems 20, 23a, and 24b

These are intersections; to find the intersection of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in both of the given sets. Remember, the empty set is { }.
Problems 22

These are complements; the universe and empty sets are complements.
Problems 25, 27, 30, 37, and 39

These are unions; to find the union of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in either of the given sets.
Problems 26, 28, 29, 38 and 40

These are intersections; to find the intersection of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in both of the given sets.
Problems 31-35

These are complements; remember, complement is relative to the universe.
Problems 41-46

See Figure 2.7.
Problems 47-52

See Example 1 for union and intersection; and Figure 2.2 for complement.
Problems 53-58

See Example 3. Draw two interlocking circles within a rectangle representing the universe. Next, label the circles and fill in the number in the intersection first. Finally, fill in the number in the remaining regions by using subtraction.
**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/

There are many problems throughout the text labeled IN YOUR OWN WORDS.

Make sure you understand the operations of union, intersection, and complement

(**Problem 1**).

**Problem 2** is interesting because it is taken from the California Assessment Program. It is based on the formula for the cardinality of the union of two sets. Relax; do not be afraid answer using your own words.

Remember intersection is “and”, union is “or,” and complement is “not.”

You should remember both of these formulas.

Remember the conditions under which this is true.

Contrast union, intersection, and complement for the given sets.

These are complements; to find the complement of a set, look at the universe

(set U), and list all elements in the universe that are not in the given set. Notice that Problems 11 and 17 are the same, and so are Problems 12 and 18.

For multiples of three, “count by 3”; {3, 6, 9, … }

For multiples of five, “count by 5”; {5, 10, 15, … }

These are complements; to find the complement of a set, look at the universe

(set U), and list all elements in the universe that are not in the given set. Notice that Problems 11 and 17 are the same, and so are Problems 12 and 18.

These problems deal with unions, intersections, and complements.

These are unions; to find the union of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in either of the given sets. Remember, the empty set is { }.

These are intersections; to find the intersection of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in both of the given sets. Remember, the empty set is { }.

These are complements; the universe and empty sets are complements.

These are unions; to find the union of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in either of the given sets.

These are intersections; to find the intersection of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in both of the given sets.

These are complements; remember, complement is relative to the universe.

See Figure 2.7.

See Example 1 for union and intersection; and Figure 2.2 for complement.

See Example 3. Draw two interlocking circles within a rectangle representing the universe. Next, label the circles and fill in the number in the intersection first. Finally, fill in the number in the remaining regions by using subtraction.