**Problem 1**

This problem is to test your understanding of the basic concepts of this section.

**Problems 2-3**

There are two of the basic concepts of this section. Rephrase each of these ideas using your own words.

**Problem 4**

Rephrase Polya’s problem solving method in your own words using a detective solving a case as an example.

**Problems 5-8**

Compare each problem with the following reasoning forms:

**Valid reasoning:** direct reasoning, indirect reasoning, transitive reasoning **Invalid reasoning: f**allacy of the converse, fallacy of the inverse, and false chain pattern.

**Problems 9-28**

See Example 7; fit each problem into one of the types of valid or invalid reasoning: direct reasoning, indirect reasoning, transitive reasoning, fallacy of the converse, fallacy of the inverse, or false chain pattern.

**Problems 29-32**

See Example 7; fit each problem into one of the types of valid or invalid reasoning: direct reasoning, indirect reasoning, transitive reasoning, fallacy of the converse, fallacy of the inverse, or false chain pattern.

** Problems 33-36**

Set up a truth table and then list all possibilities of *p* and *q* (or for *p*, *q,* and *r* in Problems 33 and 34). Complete the truth table to prove the result (or disprove them in the case of **Problems 35 and 36** ).

**Problems 37-43**

Use direct reasoning, indirect reasoning, law of excluded middle, or transitivity to form a valid conclusion. See Examples 1-3.

**Problems 44-48**

These problems need to be translated into symbolic form before finding the conclusion. See Examples 4 and 5.

**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/