(a) Prove that if 151 integers are selected from {1, 2, 3, ..., 300}, then the selection...

Question:

(a) Prove that if 151 integers are selected from {1, 2, 3, ..., 300}, then the selection must include two integers x, y where x|y or y|x.
(b) Write a statement that generalizes the results of part (a) and Example 5.43.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 08:24 AM

See More Questions

(a) If 11 integers are selected from {1, 2, 3, ..., 100}, prove that there are at least two, say x and y, such that 0 < |x - y < l. (b) Write a statement that generalizes the result of part (a).
a) Show that if five integers are selected from the first eight positive integers, there must be a pair of these integers with a sum equal to 9. b) Is the conclusion in part (a) true if four integers...
(a) Show that if any 14 integers are selected from the set S = {1, 2, 3, ..., 25}, there are at least two whose sum is 26. (b) Write a statement that generalizes the results of part (a) and Example...
The functions in Exercises 1128 are all one-to-one. For each function, a. Find an equation for f -1 (x), the inverse function. b. Verify that your equation is correct by showing that f( f -1 (x)) = x...
Mamas Stuffin is a popular food item during the fall and winter months, but it is marginal in the spring and summer. Use the following demand forecasts and costs to determine which of the following...
How, if at all, should Leilani utilize input from her unit managers, supervisors, and staff to develop and implement training programs?
How will target customers find out about the business? LO.1
A scatter plot can reveal a relationship between two indicators. Construct a scatter plot of annual data beginning in 1959 for inflation and money growth. Measure these as the percent change from a...
This is an exercise in predictive analytics. Estimation of the cost function and evaluation of the cost function is an important skill for MBAs. As often happens, you will get a cost function that...
For Simonsen Village, prepare a government-wide statement of net position and statement of activities, and a governmental funds balance sheet and statement of revenues, expenditures, and changes in...
Let S = {3, 7, 11, 15, 19, ... , 95, 99, 103}. How many elements must we select from S to insure that there will be at least two whose sum is 110?
(a) If S Z+ and |S| >3, prove that there exist distinct x, y e S where x + y is even. (b) Let S Z+ Z+. Find the minimal value of |S| that guarantees the existence of distinct ordered pairs (x1,...
Calculate the multiplier and the change in real GDP. An economy has a fixed price level, no imports, and no income taxes. MPC is 0.80, and real GDP is $150 billion. Businesses increase investment by...
The following accounts appear in the ledger of Sheridan Ltd. after the books are closed at December 31 ( in thousands). Share Capital-Ordinary, no par, 1 stated value, 400,000 shares authorized;...
1. Let f(x) 223-9x2. (a) Find all critical points for f(x).
Sadie's ski shop sells ski and boots. Skis are sold for $300 per pair and have associated Variable Costs of $150 per pair. Boots are sold for $200 per pair with an associated Variable Expense of $65...
How do you apply what is learned in the Science of Branding 1 5 - 1 , Key Insights Regarding Global Brand Strategies Based on Research Findings to improve on the brand?
CASH MANAGEMENT Dr. Umburgh noticed that the $100.00 check made to Trenton Medical Supplies has not cleared for four months. What type of check is the outstanding check referred to as? a. Stale-dated...
Cycle counting is: (a) Counting a statistically significant cross-section of your inventory frequently. (b) Counting everything in your facility at least twice per calendar or fiscal year. (c)...
Provide a draft/outline of legal research involving an indigenous Canadian woman charged with assault causing bodily harm under (Sec 267b) of the Criminal Code, where the crown wants a 12-month jail...
Graph the expense and revenue functions. a. Determine an appropriate maximum horizontal-axis value. b. Determine an appropriate maximum vertical-axis value. c. Sketch the graphs of the expense and...
If each set of bivariate data has a causal relationship, determine the explanatory and response variables for each set of data. a. Number of hours spent reading and page number on which you are...
Determine the coordinates of the maximum point on the revenue graph. Round to the nearest hundredth. A company is interested in producing and selling a new device called an eyePOD (eyewear personal...
Aecerty 1067687 was completed with the folowing charaderistick Murulectere sec00 5xs:99 s35ida sputed
Assume todays settlement price on a CME EUR futures contract is $1.3180 per euro. You have a long position in one contract. EUR125,000 is the contract size of one EUR contract. Your performance bond...
Q2. Company ABC bought an equipment for $20,000 in 2015, with useful life of 5 years $5,000 residual value amortized using straight-line method. Prepare a table to illustrate the differences...

(a) Prove that if 151 integers are selected from {1, 2, 3, ..., 300}, then the selection...

Question:

Step by Step Answer:

a For each x 123 300 wrote x 2 n m where n0 and gcd 2m 1 There are 150 po...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions