The Nature of Mathematics, 12th Edition
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Homework Hints for Section 3.4

    Problems 1-3
    There test your understanding of the basic concepts of this section. ???
    Problems 4-5
    There are two of the basic concepts of this section. Rephrase each of these ideas using your own words.
    Problem 6
    Rephrase Polya's problem solving method in your own words using a detective solving a case as an example.
    Problems 7-10
    Compare each problem with the following reasoning forms: Valid reasoning: direct reasoning, indirect reasoning, transitive reasoning Invalid reasoning: fallacy of the converse, fallacy of the inverse, and false chain pattern.
    Problems 11-33
    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 34-36
    Set up a truth table and then list all possibilities of p and q (or for p, q, and r in Problem 35).  Complete the truth table to prove the result (or disprove it in the case of Problem 35 ). 
    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/

    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/

    Mathematics Home Page
    Access the Clemens and Alcuins Library of CSB/SJU and find one of the world's best collections of mathematical internet sites.
    http://library.csbsju.edu/rqs.phtml?subject_id=32

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