Problems 1-4
These problems are the Essential Ideas for this section. Work through all of these problems. See the link entitled "Venn Diagrams for 2, 3, and 4 sets" for some help with these problems.

Problems 5-8
See Example 2 of the previous section; that is, for these problems use the cardinality of the union of two sets property.

Problems 9-12
See Example 2 of the previous section.

Problems 13-16
See Example 1. Begin by filling in the cardinality of the set labeled VII. Next, fill in the cardinality of the sets labeled IV, V, and VI (in any order). Then, fill in the cardinality of the sets labeled I, II, and III. Finally, fill in the cardinality of the region labeled VIII.

Problems 17-18
Complete a Venn diagram by labeling each of the eight sections formed by the three sets in each case.

Problems 19-27 First, draw a Venn diagram (see Example 3) and then compare your Venn diagram with Figure 8.12 (which labels the eight regions). Use this Venn diagram to answer the questions in Problems 20-27.

Problems 28-36 First, draw a Venn diagram (see Example 3) and then compare your Venn diagram with Figure 8.12 (which labels the eight regions). Use this Venn diagram to answer the questions in Problems 29-36.

Problems 37-45 First, draw a Venn diagram (see Example 3). Use this Venn diagram to answer the questions in
Problems 38-45.

Problems 46-53 First, draw a Venn diagram (see Example 3). Use this Venn diagram to answer these questions.

Problem 54 Begin with the Venn diagram; the categories are black parents, white parents, and Hispanic parents. The intersection of the cirle of "black" and "white" would be those people with 1 black parent and 1 white parent. The intersection of all three of these sets is empty. After you have the Venn diagram, calculate the number in each of the eight regions.

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