Explanation Given information: To describe the circumstances for the above sentences to be paradoxical, assume the following: Mr. N says statement ( i ) and Mr. J says statement ( ii ) about Watergate. All other assertions of Mr. N are equally split between true and false. That ¡s, sentence ( ii ) is either true or false. Concept used: In general, in the implication, A → B ( if A then B ) , A stands for the antecedent, and, B stands for the consequent. Calculation: Consider the following two sentences: ( i ) Most of Mr. N assertions about Watergate are false. ( ii ) Everything Mr. J says about Watergate is true. Note that sentence ( ii ) is also an assertion about Watergate. To describe the circumstances for the above sentences to be paradoxical, assume the following: Mr. N says statement ( ii ) and Mr. J says statement ( i ) about Watergate. All other assertions of Mr. N are equally split between true and false. That is, sentence ( i ) is either true or false

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ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 6.4, Problem 23ES

To determine

Most of Nixon’s assertions about Watergate are false.

Everything Jones says about Watergate is true.

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Chapter 6.4, Problem 22ES

Chapter 6.4, Problem 24ES

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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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Most of Nixon’s assertions about Watergate are false. Everything Jones says about Watergate is true.

Solution Summary: The author explains that Nixon's assertions about Watergate are false, and everything Jones says about it is true.