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Chapter 1 Exercises:

1) In the manufacture of a certain type of automobile, four kinds of major defects and seven kinds of minor defects can occur. For those situations in which defects do occur, in how many ways can there be twice as many minor defects as there are major ones?

If there are 4 major and 7 minor defects, there are 3 ways that there could be twice as many minor defects as major ones.

major = 1, minor = 2 major = 2, minor = 4 major = 3, minor = 6

2) A machine has nine different dials, each with five settings labeled 0, 1, 2, 3, and 4. a) In how many ways can all the dials on the machine be set?

5^9 = 1,953,125

Chapter 2 Exercises:

2.1.2) Identify the primitive statements in Exercise 1. The following statements are primitive because they are broken down to the simplest form: (a) In 2003 George W. Bush was the president of the United States
(c) Fifteen is an even number (f) As of June 30, 2003, Christine Marie Evert had won the French Open a record second times.

2.2.2) Verify the first Absorption Law by means of a truth table. p v (p^q) <=> p

p | q | p^q | pv(p^q) | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | p ^ (pvq) <=> p

p | q | pvq | p^(pvq) | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |

2.3.4) For each of the following pairs of statements, use Modus Ponens or Modus Tollens to fill in the blank line so that a valid argument is presented.

a) If Janice has trouble starting her car, then her daughter Angela will check
Janice’s spark plugs. Janice had trouble starting her car. (Modes Ponens)

b) If Brady