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### review_1

Course: MATH 105, Winter 2009
School: Walla Walla University
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Word Count: 709

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I Exam Review Sheet MATH 105, Spring 2003 This exam will cover sections 3.1-4.5 in your text. You should know general terms and denitions from each of these sections, review the homework and quizzes given for these sections, and pay particular attention to the subjects and practice problems mentioned below. 1. Dening sets using descriptions, the roster method, and set-builder notation. 2. Working with universal...

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I Exam Review Sheet MATH 105, Spring 2003 This exam will cover sections 3.1-4.5 in your text. You should know general terms and denitions from each of these sections, review the homework and quizzes given for these sections, and pay particular attention to the subjects and practice problems mentioned below. 1. Dening sets using descriptions, the roster method, and set-builder notation. 2. Working with universal sets and subsets. 3. Analyzing weighted voting scenarios similar to those found in your text. 4. Combining sets with standard set operations. 5. Using Venn Diagrams to combine sets and to count 6. Translating between symbolic logic and English. 7. Working with truth tables. 8. Working with conditional sentences both in English and symbolically. 9. Basic valid and invalid arguments. Below is a list of sample problems. This list is not all-inclusive, but does represent the basic types of problems you may see on the exam. 1. Identify the type of notation used to write each of the sets below, and then write the same set it the two remaining notations. (a) Let R be the set of all colors of the rainbow. (b) {x | x is an Adventist College in the U.S.} (c) {2, 3, 5, 7, 11, . . .} 2. Let U be the set of all WWC students, the universal set for the following instances. (a) Give two proper subsets of U . (b) Suppose that the set F = {x U | x is friendly}. Is this set well dened? Why or why not? (c) Let S be the set of all former WWC student missionaries and T the set of WWC students who have traveled abroad. Suppose that you suspected S = T . How would you show this? (d) If P = {T om, Jane, Bill, Joe} are all WWC students who would like to go to the movies with you, in how many ways can you pick people from this group to accompany you? (e) If A is any subset of U , what set is always a subset of A? 3. Consider the weighted voting scheme [6 : 4, 3, 2, 1] and answer the following questions. (a) What are the losing coalitions? (b) Does any voter no have power? (c) Is any voter a dictator? 4. Suppose that P = {2, 3, 5, 7, 9, 11}, E = {2, 4, 6, 8, 10, 12}, O = {1, 3, 5, 7, 9, 11} and U = {1, 2, . . .12} is the universal set. Find the following sets. (a) P O (d) E P (g) (P E) (j) O E (b) P O (e) E P (h) (O P ) E (k) U E 1 (c) E (f) (E P ) (i) O (P E) (l) O 5. Use Venn Diagrams to determine if the following sets are equal. (a) A (B C) and (A B) (A C). (b) A B and (A B) (c) A B and A B 6. Suppose that you surveyed 150 students asking them if they attended vespers, church, and chapel during a given week. Of these students, 75 attended vespers, 92 attended church, and 121 attended chapel. 43 attended both vespers and church, 80 attended both church and chapel, and 61 attended both vespers and chapel. 36 attended all three. Construct a Venn Diagram and use it to answer the following questions. (a) How many attended vespers and church, but not chapel? (b) How many attended none of the three events? (c) How many attended exactly one event? (d) How many attended at least two of the events? 7. Suppose that p : you vote in the next election, and q : you are an informed elector. State each of the...

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