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Textbook Exercises

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Week 1 Textbook Exercises
Jessica Pollock
MTH/221
October 28, 2013
Leslie Fife

Week 1 Textbook Exercises
Chapter 1 Supplementary Exercises
#7. There are 12 men at a dance. (a) In how many ways can eight of them be selected to form a cleanup crew?
Order does not matter
Cannot repeat
N = 12 R = 8

(b) How many ways are there to pair off eight women at the dance with eight of these 12 men?
Order does matter
Cannot repeat
N = 12 R = 8

Exercises 2.1 #3
Let p,q be primitive statements for which the implication is false. Determine the truth values for each of the following. a. = false
True and false

b. = false not true or false c. = true
False implies true d. = false
Not false implies not true
Exercises 2.2 #17
For any statements p,q, prove that a. P | q | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |

b. p | q | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |

Exercises 2.3 #1
The following are three valid arguments. Establish the validity of each by means of a truth table. In each case, determine which rows of the table are crucial for assessing the validity of the argument and which rows can be ignored. a. P | Q | R` | | | | | | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Argument validity is from result of last row. All other rows can be ignored. b. P | Q | R | | | | | | | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 |

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