Explanation Given: Preference table with changes in last column from question 13 as shown below Number of votes 70 60 50 30 First choice C B A C Second Choice A C B A Third choice B A C B Explanation: According to the Plurality-with-elimination method, the candidate with majority of first place votes is the winner. If no candidate receives majority of first place votes eliminate the candidate with fewer votes from the preference table and move up the candidates below the eliminated candidate in each column. The candidates with majority of first place votes is winner. If again no candidate gets majority of votes then whole process is repeated until a candidate with majority votes is found. Let’s determine the winner, First, calculate total number of votes 70 + 60 + 50 + 30 = 210 Therefore, majority votes ( 50 % of total votes) = 105 Number of votes 70 60 50 30 First choice C B A C Second Choice A C B A Third choice B A C B Now, Let’s calculate votes for each candidate as first choice, A receives 50 votes B receives 60 votes C receives 70 + 30 = 100 votes Observe that none of the candidate receives majority votes. Thus, eliminate A from preference table as A receives least votes and make a new preference table, Number of votes 70 60 50 30 First choice C B B C Second Choice B C C B Again, Let’s calculate votes for each candidate as first choice, B receives 60 + 50 = 110 votes C receives 70 + 30 = 100 votes Thus, B receives majority of first choice votes

Thinking Mathematically, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package, 4/e (7th Edition)

7th Edition

ISBN: 9780135222249

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 13, Problem 14T

To determine

Winner using Plurality-with-elimination method and check whether monotonicity criterion is satisfied or not.

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Chapter 13, Problem 13T

Chapter 13, Problem 15T

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1. 2. Show that the following are not logically equivalent by finding a counterexample: (p^q) →r and (db) V (d←d) Show that the following is not a contradiction by finding a counterexample: (pV-q) AqA (pv¬q Vr) 3. Here is a purported proof that (pq) ^ (q → p) = F: (db) v (bd) = (db) v (bd) =(qVp) A (g→p) = (¬¬q V ¬p) ^ (q→ p) (db) V (db) = =¬(a→p)^(a→p) = (gp) ^¬(a → p) =F (a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex- ample. (b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps with their corresponding laws of propositional logic.

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Chapter 13 Solutions

Thinking Mathematically, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package, 4/e (7th Edition)

Ch. 13.1 - CHECK POINT 1 Four candidates are running for...Ch. 13.1 - CHECK POINT 2 Table 13.2 on page 841 shows the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - CHECK POINT 5 Table 13.2 on page 841 shows the...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...

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