3rd Edition

ISBN: 9780131679955

Author: Edgar G. Goodaire

Publisher: Prentice Hall

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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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Textbook Question

Chapter 4.3, Problem 33E

Show that there are infinitely many triples of integers a , b , c that satisfy a 2 + b 2 = c 2 .

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Chapter 4.3, Problem 32E

Chapter 4.3, Problem 34E

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A ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.

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Chapter 4 Solutions

Discrete Mathematics with Graph Theory

Ch. 4.1 - 227 Ch. 4.1 - The Well-Ordering Principle states that any...Ch. 4.1 - Prob. 3TFQ Ch. 4.1 - Prob. 4TFQ Ch. 4.1 - Prob. 5TFQ Ch. 4.1 - Prob. 6TFQ Ch. 4.1 - Prob. 7TFQ Ch. 4.1 - Prob. 8TFQ Ch. 4.1 - Prob. 9TFQ Ch. 4.1 - Prob. 10TFQ

Ch. 4.1 - Prob. 1E Ch. 4.1 - 2. True or false? If false, give a counterexample....Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - 9. Suppose is a natural number and is the...Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.2 - True/False Questions Given two consecutive...Ch. 4.2 - Prob. 2TFQ Ch. 4.2 - Prob. 3TFQ Ch. 4.2 - Prob. 4TFQ Ch. 4.2 - Prob. 5TFQ Ch. 4.2 - Prob. 6TFQ Ch. 4.2 - Prob. 7TFQ Ch. 4.2 - Prob. 8TFQ Ch. 4.2 - Prob. 9TFQ Ch. 4.2 - Prob. 10TFQ Ch. 4.2 - Prob. 1E Ch. 4.2 - Prob. 2E Ch. 4.2 - Draw the Hasse diagrams for each of the following...Ch. 4.2 - List all minimal, minimum, maximal, and maximum...Ch. 4.2 - Let n be a natural number. Given n consecutive...Ch. 4.2 - Prove that n22(n an integer) is never divisible by...Ch. 4.2 - Given that a and x are integers, a1, a|(11x+3),...Ch. 4.2 - Prob. 8E Ch. 4.2 - Prob. 9E Ch. 4.2 - Prob. 10E Ch. 4.2 - Prob. 11E Ch. 4.2 - Prob. 12E Ch. 4.2 - Prob. 13E Ch. 4.2 - If a and b are relatively prime integers, prove...Ch. 4.2 - Prob. 15E Ch. 4.2 - Prob. 16E Ch. 4.2 - 17. (a) Find a pair of integers and such that ....Ch. 4.2 - Prob. 18E Ch. 4.2 - Prob. 19E Ch. 4.2 - Prob. 20E Ch. 4.2 - Prob. 21E Ch. 4.2 - If aN, prove that...Ch. 4.2 - Prob. 23E Ch. 4.2 - Prob. 24E Ch. 4.2 - Prob. 25E Ch. 4.2 - Prob. 26E Ch. 4.2 - Prob. 27E Ch. 4.2 - Prob. 28E Ch. 4.2 - Prob. 29E Ch. 4.2 - Prob. 30E Ch. 4.2 - Establish formula (2) of this section by proving...Ch. 4.2 - Prob. 32E Ch. 4.2 - Suppose a,b,c are nonzero integers. Show that...Ch. 4.2 - 34. Suppose that and are partial orders. (a)...Ch. 4.2 - Prob. 35E Ch. 4.2 - Let g be the greatest common divisor of integers m...Ch. 4.3 - 127 is a prime number.Ch. 4.3 - Prob. 2TFQ Ch. 4.3 - Prob. 3TFQ Ch. 4.3 - Prob. 4TFQ Ch. 4.3 - Prob. 5TFQ Ch. 4.3 - Prob. 6TFQ Ch. 4.3 - Prob. 7TFQ Ch. 4.3 - Prob. 8TFQ Ch. 4.3 - Prob. 9TFQ Ch. 4.3 - Prob. 10TFQ Ch. 4.3 - Determine whether each of the following integers...Ch. 4.3 - Prob. 2E Ch. 4.3 - Suppose p is the smallest prime factor of an...Ch. 4.3 - Prob. 4E Ch. 4.3 - Prob. 5E Ch. 4.3 - Prob. 6E Ch. 4.3 - Prob. 7E Ch. 4.3 - Prob. 8E Ch. 4.3 - Prob. 9E Ch. 4.3 - Prob. 10E Ch. 4.3 - Prob. 11E Ch. 4.3 - Prob. 12E Ch. 4.3 - Estimate the number of primes less than 5000, less...Ch. 4.3 - Prob. 14E Ch. 4.3 - Prob. 15E Ch. 4.3 - Prob. 16E Ch. 4.3 - Prob. 17E Ch. 4.3 - 18. (a) Is prime? Explain your answer. (b) Is...Ch. 4.3 - Prob. 19E Ch. 4.3 - Prob. 20E Ch. 4.3 - 21. Show that the sum of two consecutive primes is...Ch. 4.3 - Prob. 22E Ch. 4.3 - Prob. 23E Ch. 4.3 - Prob. 24E Ch. 4.3 - Prob. 25E Ch. 4.3 - Prob. 26E Ch. 4.3 - Let p1p2.......pn+1 denote the first n+1 primes...Ch. 4.3 - Prob. 28E Ch. 4.3 - Prob. 29E Ch. 4.3 - Let a and b be natural numbers. Find the prime...Ch. 4.3 - Prob. 31E Ch. 4.3 - Prob. 32E Ch. 4.3 - 33. Show that there are infinitely many triples of...Ch. 4.3 - Prob. 34E Ch. 4.3 - Prob. 35E Ch. 4.3 - 36. Let denote the set of positive rational...Ch. 4.3 - Prob. 37E Ch. 4.3 - Prob. 38E Ch. 4.4 - A 2003 country music hit by Alan Jackson and Jimmy...Ch. 4.4 - Prob. 2TFQ Ch. 4.4 - Prob. 3TFQ Ch. 4.4 - 4. Ch. 4.4 - Prob. 5TFQ Ch. 4.4 - There are 72 congruence classes of integers mod...Ch. 4.4 - Prob. 7TFQ Ch. 4.4 - Prob. 8TFQ Ch. 4.4 - Prob. 9TFQ Ch. 4.4 - Prob. 10TFQ Ch. 4.4 - Prob. 1E Ch. 4.4 - Prob. 2E Ch. 4.4 - Prob. 3E Ch. 4.4 - 4. True or False? Give a reason for each answer....Ch. 4.4 - Prob. 5E Ch. 4.4 - Prob. 6E Ch. 4.4 - Prob. 7E Ch. 4.4 - Prob. 8E Ch. 4.4 - Find all integers x, 0xn, satisfying each of the...Ch. 4.4 - 10. (a) Given integers and a prime , suppose ....Ch. 4.4 - 11. Find all integers and, , that satisfy each of...Ch. 4.4 - Prob. 12E Ch. 4.4 - Prob. 13E Ch. 4.4 - Prob. 14E Ch. 4.4 - Prob. 15E Ch. 4.4 - Prob. 16E Ch. 4.4 - Prob. 17E Ch. 4.4 - Find all integers x, 0xn, that satisfy each of the...Ch. 4.4 - Find all integers x,0xn, that satisfy each of the...Ch. 4.4 - Find all integers x,0xn, that satisfy each of the...Ch. 4.4 - In each case, find the inverse of a(modn) and use...Ch. 4.4 - In each of the following the given integer p is a...Ch. 4.4 - 23. Show that has no solutions. Ch. 4.4 - 24. Let A be the set of congruence classes of...Ch. 4.5 - Prob. 1TFQ Ch. 4.5 - Prob. 2TFQ Ch. 4.5 - Prob. 3TFQ Ch. 4.5 - Prob. 4TFQ Ch. 4.5 - Prob. 5TFQ Ch. 4.5 - Prob. 6TFQ Ch. 4.5 - Prob. 7TFQ Ch. 4.5 - Prob. 8TFQ Ch. 4.5 - Prob. 9TFQ Ch. 4.5 - Prob. 10TFQ Ch. 4.5 - Prob. 1E Ch. 4.5 - Prob. 2E Ch. 4.5 - Prob. 3E Ch. 4.5 - Prob. 4E Ch. 4.5 - Prob. 5E Ch. 4.5 - Prob. 6E Ch. 4.5 - Prob. 7E Ch. 4.5 - Prob. 8E Ch. 4.5 - Prob. 9E Ch. 4.5 - Prob. 10E Ch. 4.5 - Prob. 11E Ch. 4.5 - Prob. 12E Ch. 4.5 - Prob. 13E Ch. 4.5 - Prob. 14E Ch. 4.5 - Prob. 15E Ch. 4.5 - Prob. 16E Ch. 4.5 - Prob. 17E Ch. 4.5 - 18. In each case, find the smallest nonnegative...Ch. 4.5 - For each of the following, find the smallest...Ch. 4.5 - Prob. 20E Ch. 4.5 - In each of the following cases, find a positive...Ch. 4.5 - Prob. 22E Ch. 4.5 - Prob. 23E Ch. 4.5 - Prob. 24E Ch. 4.5 - 25. Suppose. Decode each of the following encoded...Ch. 4 - Find the quotient and remainder when...Ch. 4 - Convert (1100101)2 to base 10. Convert 32,145 to...Ch. 4 - Prob. 3RE Ch. 4 - An integer n, which has exactly eight factors, is...Ch. 4 - Prob. 5RE Ch. 4 - Prob. 6RE Ch. 4 - Prob. 7RE Ch. 4 - Prob. 8RE Ch. 4 - Illustrate the Euclidean algorithm by showing that...Ch. 4 - Prob. 10RE Ch. 4 - Prob. 11RE Ch. 4 - Prob. 12RE Ch. 4 - 13. Suppose. Show that is not the sum of three...Ch. 4 - Prob. 14RE Ch. 4 - Prob. 15RE Ch. 4 - Prob. 16RE Ch. 4 - Prob. 17RE Ch. 4 - 18. What is the last digit of ? [Hint: You want...Ch. 4 - Prob. 19RE Ch. 4 - Prob. 20RE Ch. 4 - Compute 380(mod7). Find all integers x such that...Ch. 4 - Prob. 22RE Ch. 4 - Prob. 23RE Ch. 4 - Prob. 24RE Ch. 4 - Prob. 25RE Ch. 4 - Prob. 26RE Ch. 4 - Find the smallest positive integer x that...

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