(a) Explanation Obtain the preference table with the candidates that do not include C is shown below in Table 1. Use Plurality method and obtain the winner, based on the constructed table 1. By plurality method, the candidate who receives the highest votes is declared as the winner... (b) To determine To check : Whether the candidate determined in part (a) wins the election against candidate C. (c) To determine To obtain: The way the voters who support C vote insincerely to enable C to win.

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ISBN: 9780134112183

Author: RUNDE

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Question

Chapter 14.2, Problem 38E

(a)

To determine

To find: The candidate who win the runoff election, A or B, with the help of plurality method.

(b)

To determine

To check: Whether the candidate determined in part (a) wins the election against candidate C.

(c)

To determine

To obtain: The way the voters who support C vote insincerely to enable C to win.

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Chapter 14.2, Problem 37E

Chapter 14.3, Problem 1E

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- Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., p-1 2 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). 23 32 how come? The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. The set T is the subset of these residues exceeding So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1.

Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., 2 p-1 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. 23 The set T is the subset of these residues exceeding 2° So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1. how come?

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Chapter 14 Solutions

EBK SURVEY OF MATHEMATICS WITH APPLICAT

Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - Prob. 5E Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Plurality Three candidates are running for mayor...Ch. 14.1 - Prob. 10E

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The candidate who win the runoff election, A or B, with the help of plurality method.

Solution Summary: The author explains how to obtain the candidate who wins the runoff election, A or B, with the help of plurality method.

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To find: The candidate who win the runoff election, A or B, with the help of plurality method.

To check: Whether the candidate determined in part (a) wins the election against candidate C.

To obtain: The way the voters who support C vote insincerely to enable C to win.

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Chapter 14 Solutions