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
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 7.6, Problem 8E
Without any calculation, prove that
n!=Dn+(n2)Dn−1+(n2)Dn−2+.....+(nn−1)D1+1
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem 11 (a) A tank is discharging water through an orifice at a depth of T
meter below the surface of the water whose area is A m². The
following are the values of a for the corresponding values of A:
A 1.257 1.390
x 1.50 1.65
1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650
1.80 1.95 2.10 2.25 2.40 2.55 2.70
2.85
Using the formula
-3.0
(0.018)T =
dx.
calculate T, the time in seconds for the level of the water to drop
from 3.0 m to 1.5 m above the orifice.
(b) The velocity of a train which starts from rest is given by the fol-
lowing table, the time being reckoned in minutes from the start
and the speed in km/hour:
| † (minutes) |2|4 6 8 10 12
14 16 18 20
v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0
Estimate approximately the total distance ran in 20 minutes.
-
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?
Chapter 7 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 7.1 - True/False Questions 5!=120Ch. 7.1 - Prob. 2TFQCh. 7.1 - Prob. 3TFQCh. 7.1 - Prob. 4TFQCh. 7.1 - Prob. 5TFQCh. 7.1 - Prob. 6TFQCh. 7.1 - True/False Questions
7. An r-permutation of n...Ch. 7.1 - Prob. 8TFQCh. 7.1 - Prob. 9TFQCh. 7.1 - True/False Questions There are 4!=24 ways in which...
Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - In how many ways can ten boys and four girls sit...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - [BB] In how many ways can two couples, the...Ch. 7.1 - Repeat Exercise 12, assuming, in each part, that a...Ch. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - 17. (a) In how many numbers with seven distinct...Ch. 7.1 - Prob. 18ECh. 7.2 - True/False Questions
Ch. 7.2 - Prob. 2TFQCh. 7.2 - Prob. 3TFQCh. 7.2 - Prob. 4TFQCh. 7.2 - Prob. 5TFQCh. 7.2 - Prob. 6TFQCh. 7.2 - Prob. 7TFQCh. 7.2 - Prob. 8TFQCh. 7.2 - Prob. 9TFQCh. 7.2 - Prob. 1ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 3ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - [BB] In how many ways can Tom, Billie, and Peter...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - 7. In a popular lottery known as Lotto 6/49, a...Ch. 7.2 - Prob. 8ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - 16. The head of the Department of Mathematical...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.3 - Prob. 1TFQCh. 7.3 - Prob. 2TFQCh. 7.3 - Prob. 3TFQCh. 7.3 - Prob. 4TFQCh. 7.3 - Prob. 5TFQCh. 7.3 - Prob. 6TFQCh. 7.3 - Prob. 7TFQCh. 7.3 - Prob. 8TFQCh. 7.3 - Prob. 9TFQCh. 7.3 - Prob. 10TFQCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - [BB] A fair coin is tossed six times. Find the...Ch. 7.3 - Prob. 6ECh. 7.3 - The next two exercises refer to Lotto 6/49, a...Ch. 7.3 - 8. In Lotto 6/49, find the probability of...Ch. 7.3 - 9. [BB] A basket contains five red balls, four...Ch. 7.3 - Prob. 10ECh. 7.3 - [BB] Repeat Exercise 9 assuming the first ball...Ch. 7.3 - 12. Repeat Exercise 10 assuming the two balls are...Ch. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Find the probability that an integer selected at...Ch. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - (See Exercise 11 of Section 7.1), find the...Ch. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.4 - Prob. 1TFQCh. 7.4 - Prob. 2TFQCh. 7.4 - Prob. 3TFQCh. 7.4 - Prob. 4TFQCh. 7.4 - Prob. 5TFQCh. 7.4 - Prob. 6TFQCh. 7.4 - Prob. 7TFQCh. 7.4 - Prob. 8TFQCh. 7.4 - Prob. 9TFQCh. 7.4 - Prob. 10TFQCh. 7.4 - Prob. 1ECh. 7.4 - 2. If the die in Exercise 1 is tossed twice, find...Ch. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - [BB] A coin has P(H)=14. If it is tossed six times...Ch. 7.4 - The answers to exercises marked [BB] can be found...Ch. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - 15. A fair coin is tossed n times. Let A be the...Ch. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - 22. (a) Find the probability that everyone in a...Ch. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - [BB] Given 70P20=.3,40P50=.5, and 10P40=.9, find...Ch. 7.4 - [BB] The probability that two persons aged 20 and...Ch. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - 29. [BB] Consumers in the town of Trout River have...Ch. 7.4 - Prob. 30ECh. 7.4 - 31. A new three- screen cinema has just opened in...Ch. 7.5 - Prob. 1TFQCh. 7.5 - (Answers can be found in the back of the book.)
2....Ch. 7.5 - (Answers can be found in the back of the book.)...Ch. 7.5 - Prob. 4TFQCh. 7.5 - Prob. 5TFQCh. 7.5 - Prob. 6TFQCh. 7.5 - Prob. 7TFQCh. 7.5 - Prob. 8TFQCh. 7.5 - Prob. 9TFQCh. 7.5 - Prob. 10TFQCh. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - 6. Twenty varieties of chocolates are available...Ch. 7.5 - Prob. 7ECh. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 10ECh. 7.5 - 11. (a) [BB] In how many ways can ten red balls,...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 13ECh. 7.5 - Find the number of arrangements of the letters of...Ch. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Show that there is a one-to-one correspondence...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 19ECh. 7.6 - (Answers can be found in the back of the book.)
1....Ch. 7.6 - Prob. 2TFQCh. 7.6 - Prob. 3TFQCh. 7.6 - Prob. 4TFQCh. 7.6 - Prob. 5TFQCh. 7.6 - Prob. 6TFQCh. 7.6 - (Answers can be found in the back of the book.)
7....Ch. 7.6 - Prob. 8TFQCh. 7.6 - Prob. 9TFQCh. 7.6 - Prob. 10TFQCh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - [BB] In how many ways can the integers 1 through 9...Ch. 7.6 - Without any calculation, prove that...Ch. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.7 - (Answers can be found in the back of the book.)
1....Ch. 7.7 - Prob. 2TFQCh. 7.7 - Prob. 3TFQCh. 7.7 - Prob. 4TFQCh. 7.7 - Prob. 5TFQCh. 7.7 - Prob. 6TFQCh. 7.7 - Prob. 7TFQCh. 7.7 - Prob. 8TFQCh. 7.7 - Prob. 9TFQCh. 7.7 - Prob. 10TFQCh. 7.7 - Prob. 1ECh. 7.7 - The answers to exercises marked [BB] can be found...Ch. 7.7 - Prob. 3ECh. 7.7 - Prob. 4ECh. 7.7 - Prob. 5ECh. 7.7 - Prob. 6ECh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Prob. 9ECh. 7.7 - Prob. 10ECh. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Sequences of integers, {xn},{yn},n0, are defined...Ch. 7.7 - Prob. 15ECh. 7.7 - The answers to exercises marked [BB] can be found...Ch. 7.7 - Prob. 17ECh. 7.7 - 18. Prove the Binominal Theorem by mathematical...Ch. 7.7 - Prob. 19ECh. 7.7 - Prob. 20ECh. 7.7 - Prob. 21ECh. 7.7 - Prob. 22ECh. 7.7 - Prob. 23ECh. 7.7 - 24. There are n books in a line on a shelf and...Ch. 7.7 - Prob. 25ECh. 7 - Prove that 2nP(2n,n) for all integers n1.Ch. 7 - In how many ways can seven boys and six girls...Ch. 7 - Do Exercise 2 again with circle instead of row.Ch. 7 - How many permutations of the letters a, b, c, d,...Ch. 7 - 5. (a) In how many permutations of the 26...Ch. 7 - 6. Find an expression for the number of five-card...Ch. 7 - A committee of seven is to be chosen from eight...Ch. 7 - In how many ways can 12 people from four groups of...Ch. 7 - A car manufacturer is forced to admit that the...Ch. 7 - 10. Ten students find themselves in an...Ch. 7 - 11. For Christmas, Gail wants to buy each of her...Ch. 7 - 12. A Middle East peace conference will be...Ch. 7 - Prob. 13RECh. 7 - Frank wants to buy 12 muffins and finds seven...Ch. 7 - Twelve ships enter the St. Johns harbor one after...Ch. 7 - 16. A candy merchant carries bubble gum balls in...Ch. 7 - 17. In how many ways can the letters of the word...Ch. 7 - 18. In how many ways can five rings be put onto...Ch. 7 - Find the coefficient of x6 in (16x212x)12....Ch. 7 - Find the coefficient of x6 in (16x212x)12....Ch. 7 - 21. Prove that for any .
Ch. 7 - Give a verbal argument for the truth of the...Ch. 7 - 23. Find a simple expression for .
Ch. 7 - Show that (2nn) is even for all n1.Ch. 7 - On the day before midterm break, 20 of the 32...Ch. 7 - 26. A fair coin is tossed n times. Prove that...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Shading a Venn diagram with 3 sets: Unions, intersections, and... The Venn diagram shows sets A, B, C, and the universal set U. Shade (CUA)' n B on the Venn diagram. U Explanation Check A- B Q Search 田arrow_forward3. A different 7-Eleven has a bank of slurpee fountain heads. Their available flavors are as follows: Mountain Dew, Mountain Dew Code Red, Grape, Pepsi and Mountain Dew Livewire. You fill five different cups full with each type of flavor. How many different ways can you arrange the cups in a line if exactly two Mountain Dew flavors are next to each other? 3.2.1arrow_forwardBusinessarrow_forward
- Please explain how come of X2(n).arrow_forwardNo chatgpt pls will upvotearrow_forwardFind all solutions of the polynomial congruence x²+4x+1 = 0 (mod 143). (The solutions of the congruence x² + 4x+1=0 (mod 11) are x = 3,4 (mod 11) and the solutions of the congruence x² +4x+1 = 0 (mod 13) are x = 2,7 (mod 13).)arrow_forward
- https://www.hawkeslearning.com/Statistics/dbs2/datasets.htmlarrow_forwardDetermine whether each function is an injection and determine whether each is a surjection.The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}. f: Z_(6) -> Z_(6) defined by f(x)=x^(2)+4(mod6). g: Z_(5) -> Z_(5) defined by g(x)=x^(2)-11(mod5). h: Z*Z -> Z defined by h(x,y)=x+2y. j: R-{3} -> R defined by j(x)=(4x)/(x-3).arrow_forwardDetermine whether each function is an injection and determine whether each is a surjection.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Algebraic Complexity with Less Relations; Author: The University of Chicago;https://www.youtube.com/watch?v=ZOKM1JPz650;License: Standard Youtube License
Strassen's Matrix Multiplication - Divide and Conquer - Analysis of Algorithm; Author: Ekeeda;https://www.youtube.com/watch?v=UnpySHwAJsQ;License: Standard YouTube License, CC-BY
Trigonometric Equations with Complex Numbers | Complex Analysis #6; Author: TheMathCoach;https://www.youtube.com/watch?v=zdD8Dab1T2Y;License: Standard YouTube License, CC-BY