10th Edition

ISBN: 9780134112183

Author: RUNDE

Publisher: YUZU

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Chapter 3.5, Problem 16E

In Exercises 13–32, determine whether the argument is valid or invalid. You may compare the argument to a standard form, given on page 140, or use a truth table.

16. h → i ∴ g → i g → h

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Chapter 3.5, Problem 15E

Chapter 3.5, Problem 17E

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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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In Exercises 13–32, determine whether the argument is valid or invalid. You may compare the argument to a standard form, given on page 140 , or use a truth table. 16. h → i ∴ g → i g → h

Solution Summary: The author evaluates whether the argument is valid or invalid by comparing it to the standard form or using a truth table.

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