Question: Let n Z+, n odd. If i1i2, . . . , in is a permutation of the integers 1, 2, ..., n, prove that

Let n ∈ Z+, n odd. If i1i2, . . . , in is a permutation of the integers 1, 2, ..., n, prove that (1 - i 1)(2 - i2) ∙ ∙ ∙ ∙ ∙ ∙ ∙ (n - in) is an even integer. (Which counting principle is at work here?)

Step by Step Solution

★★★★★

3.28 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

For Il n k1 ki k to be odd k i k must be odd for all 1 k n ie one of fc must be ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

954-M-L-A-L-S (7759).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let n Z+, n odd. Can a palindrome of n have an even number of summands?

Let n Z+, n even. How many palindromes of n have an even number of summands? How many have an odd number of summands?

Let p(n), q(n) represent the open statements p(n): n is odd q(n): n2 is odd for the universe of all integers. Which of the following statements are logically equivalent to each other? (a) If the...

2. Find all solutions to [39][44] + [14] [$13] = [2} in 2.91. Express your answer as [57} for some integer n: with c g: m c: 91. 3. Prove that there exist 135 consecutive positive integers chug, .. ....

MATH 135 S 2016: Assignment 9 Solutions 1. Prove that for any integer n, 441n43 + 374n35 + 285n23 0 (mod 55). Solution: Since 55 = 5 11 and gcd(5, 11) = 1, we may use the Splitting Modulus...

MAT348-Homework # 3 (20 points, due on Wednesday March 23) Question 1. Let S1 ((Z 26 )10 , (Z 26 )10 , (Z 26 )* , e (1) , d (1) ) be the multiplicative cipher defined by e(1) ( x0 ,, x9 ) (k1 x0 mod...

Just final answer will do, no need workings Q11-2 Two ordinary dice are thrown, what is the probability (in simplest fraction) that the numbers of the two dice are equal given that the sum of the...

Help 43. 45. 47. 49. 50. 51. 52. 53. 54. 55. 56. 5'7. 58. 59. of permutations of its vertices (see Example 3). Prove that S" is non-Abelian for all n a 3. . Prove that A\" is non-Abelian for all n a...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

hello please help me answer these short questions. 1. Click and drag the given steps (in the right) to their corresponding step names (in the left) to show that if a l b and bla, where a and b are...

a. Can the sign test be used with quantitative data? Why or why not? b. Can the sign test be used with ordinal data? Why or why not? c. Can the sign test be used with nominal data? Why or why not?

The process engineer for a large paint manufacturer is concerned about the consistency of an ingredient in the paint that determines the ability of the paint to resist fading. The paint has a...

Which of the following is not an aspect of Rule 2 0 1 of the General Standards of the Code of Professional Conduct? a . A member must not take on an engagement that is beyond the member's...

Economist Harvey Leibenstein argued that the loss of economic efficiency in industries that are not perfectly competitive has been understated. He argued that when competition is weak, firms are...

Enter the data from Example 1 in your calculator. a. Create a box-and-whisker plot using the data from Example 1. b. How would you determine if it would be appropriate to create a modified boxplot...

Megan has a friend at work who is selling a used Honda. The car has 60,000 miles on it. Megan comparison shops and finds these prices for the same car. a. Find the mean price of the 5 prices listed....

Megan, from Exercise 8, decides to get more information about the cars she researched. The table has prices and mileages for the same used car. In addition to the statistics she has learned in this...

The market value balance sheet for Tidwell Manufacturing is shown here. The company has declared a 10 percent stock dividend. The stock goes ex dividend tomorrow (the chronology for a stock dividend...

Your division is considering two projects with the following cash flows (in millions): 0 1 2 3 Project A -$27 $13 $17 $8 Project B -$25 $14 $11 $2 What are the projects' NPVs assuming the WACC is 5%?...

Timestamp FMG.AX 2022/4/14 $ 21.61 2022/4/13 $ 21.34 2022/4/12 $ 21.17 2022/4/11 $ 21.19 2022/4/8 $ 21.83 2022/4/7 $ 21.75 2022/4/6 $ 21.66 2022/4/5 $ 21.72 2022/4/4 $ 21.70 2022/4/1 $ 21.06...