Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.
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Chapter 6.3, Problem 26E

  1. Let A be a set of seven (distinct) natural numbers none of which exceeds 21. Prove that the sums of the elements in all the nonempty subsets of A are not distinct.

  2. Improve the result of (a) by showing that the result holds under the assumption that the integers of A do not exceed 23.

  3. Assume none of the elements of A exceeds 12. At least how many subsets of A must have the same sum?

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Chapter 6 Solutions

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 6.1 - Prob. 1TFQCh. 6.1 - Prob. 2TFQCh. 6.1 - Prob. 3TFQCh. 6.1 - Prob. 4TFQCh. 6.1 - Prob. 5TFQCh. 6.1 - Prob. 6TFQCh. 6.1 - Prob. 7TFQCh. 6.1 - Prob. 8TFQCh. 6.1 - True/False Questions 9. When three sets are...Ch. 6.1 - Prob. 10TFQ
Ch. 6.1 - In a group of 15 pizza experts, ten like...Ch. 6.1 - Prob. 2ECh. 6.1 - Among the 30 students registered for a course in...Ch. 6.1 - Prob. 4ECh. 6.1 - The owner of a corner store stocks popsicles, gum,...Ch. 6.1 - 6. (a) In a group of 82 students, 59 are taking...Ch. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - The owner of a convenience store reports that of...Ch. 6.1 - Prob. 10ECh. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Find the number of integers between 1 and 10,000...Ch. 6.1 - 16. How many integers between 1 and (inclusive)...Ch. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prove the Principle of Inclusion-Exclusion by...Ch. 6.2 - Prob. 1TFQCh. 6.2 - Prob. 2TFQCh. 6.2 - Prob. 3TFQCh. 6.2 - Prob. 4TFQCh. 6.2 - Prob. 5TFQCh. 6.2 - Prob. 6TFQCh. 6.2 - Prob. 7TFQCh. 6.2 - Prob. 8TFQCh. 6.2 - Prob. 9TFQCh. 6.2 - Prob. 10TFQCh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - 3. In how many of the three-digit numbers 000-999...Ch. 6.2 - How many numbers in the range 100-999 have no...Ch. 6.2 - Prob. 5ECh. 6.2 - 6. In Mark Salas, the 1991 Detroit Tigers had...Ch. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - How many possible telephone numbers consist of...Ch. 6.2 - Prob. 11ECh. 6.2 - 12. In how many ways can two adjacent squares be...Ch. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - How many three-digit numbers contain the digits 2...Ch. 6.2 - 16. You are dealt four cards from a standard deck...Ch. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - In how many ways can two dice land? In how many...Ch. 6.2 - Prob. 20ECh. 6.2 - How many five-digit numbers can be formed using...Ch. 6.2 - Prob. 22ECh. 6.2 - The complete menu from a local gourmet restaurant...Ch. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.3 - True/False Questions If A and B are finite...Ch. 6.3 - Prob. 2TFQCh. 6.3 - True/False Questions 3. In a group of 15 people,...Ch. 6.3 - Prob. 4TFQCh. 6.3 - True/False Questions If two integers lie in the...Ch. 6.3 - Prob. 6TFQCh. 6.3 - Prob. 7TFQCh. 6.3 - Prob. 8TFQCh. 6.3 - Prob. 9TFQCh. 6.3 - Prob. 10TFQCh. 6.3 - Prob. 1ECh. 6.3 - Write down any six natural numbers. Verify that...Ch. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - 7. (a) If 20 processors are interconnected and...Ch. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - 11. Brad has five weeks to prepare for his...Ch. 6.3 - Linda has six weeks to prepare for an examination...Ch. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Let S={2,3,5,7,11,13,17,19} be the set of prime...Ch. 6.3 - Given any positive integer n, show that some...Ch. 6.3 - 22. Show that some multiple of 2002 consists of a...Ch. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - In a room where there are more than 50 people with...Ch. 6.3 - 26. (a) Let A be a set of seven (distinct) natural...Ch. 6.3 - Prob. 27ECh. 6.3 - 28. Suppose are 10 integers between 1 and 100...Ch. 6.3 - Prob. 29ECh. 6.3 - 30. Given any 52 integers, show that there exist...Ch. 6 - Suppose A and B are nonempty finite sets and ....Ch. 6 - Using the Principle of Inclusion-Exclusion, find...Ch. 6 - John Sununu was once the governor of New...Ch. 6 - 4. Two Math 2320 students are arguing about the...Ch. 6 - Prob. 5RECh. 6 - 6. Seventy cars sit on a parking lot. Thirty have...Ch. 6 - State the strong form of the Pigeonhole Principle.Ch. 6 - 8. Show that among 18 arbitrarily chosen integers...Ch. 6 - Use the Pigeonhole Principle and the definition of...Ch. 6 - Show that, of any ten points chosen within an...Ch. 6 - Five hermits live on a rectangular island 6...Ch. 6 - 12. (a) Suppose the positive integer is written...
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