Let m and n be positive integers- Prove that mZ nZ - kZ- Where k is t.docx

•Download as DOCX, PDF•

0 likes•51 views

Let m and n be positive integers. Prove that mZ nZ = kZ. Where k is the term of m and n. Solution kZ is a set consisting of all multiples of k. Let, a Â Â (mZ Intersection nZ) So, m divides a, and also n divides a We need to show that lcm(m,n)=k also divides a. Lets use Division Algorithm: a = pk + r ------------- Equation (1) where p and r are integers such that 0 <= r < k (by <=Â Â i mean greater than or equal to) Since a is a multiple of both m and n, so lcm(m,n) divides a. So, k divides L.H.S. of equation(1) Also, k divides pk. So, k must divide r. But since r <k, So r = 0 Hence, from equation(1),Â Â a = pk So, k divides a Now we choosed a as arbitrary element in (mZ Intersection nZ), and we showed that its in kZ, So mZ Intersection nZ is contained in kZ. Now to show kZ is contained in mZ Intersection nZ. Let, b kZ So, b is a multiple of k So, b is a multiple of lcm(m.n) So, b is a multiple of both m and n. So, b is element of both mZ and nZ. Hence b lies in (mZ Intersection nZ). Since b is arbitrary element of kZ. So kZ is contained in (mZ Intersection nZ). Hence kZ = (mZ Intersection nZ) Hence we proved. :) .

Education

Now we choosed a as arbitrary element in (mZ Intersection nZ), and we showed that its in kZ,
So mZ Intersection nZ is contained in kZ.
Now to show kZ is contained in mZ Intersection nZ.
Let, b kZ
So, b is a multiple of k
So, b is a multiple of lcm(m.n)
So, b is a multiple of both m and n.
So, b is element of both mZ and nZ.
Hence b lies in (mZ Intersection nZ).
Since b is arbitrary element of kZ.
So kZ is contained in (mZ Intersection nZ).
Hence kZ = (mZ Intersection nZ)
Hence we proved.
:)

Similar to Let m and n be positive integers- Prove that mZ nZ - kZ- Where k is t.docx

Eigenvalues

Tarun Gehlot

IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.

Construction of BIBD’s Using Quadratic Residues

iosrjce

Ch05 1

Rendy Robert

Basic Introduction to Algebraic Geometry

APPLE495596

machinelearning project

Lianli Liu

04_AJMS_330_21.pdf

BRNSS Publication Hub

Solutions Manual for An Introduction To Abstract Algebra With Notes To The Fu...

Proofs nearest rank

Klt

Cis435 week03

PART VII.3 - Quantum Electrodynamics

Maurice R. TREMBLAY

Imc2017 day1-solutions

Christos Loizos

Iterative methods

Kt Silva

Binomial Theorem, Recursion ,Tower of Honai, relations

Lemh1a1

Lemh1a1

Number theory

Solution baupc 1999

Z transform and Properties of Z Transform

AnujKumar734472

lec z-transform.ppt

MohammadRefai6

Similar to Let m and n be positive integers- Prove that mZ nZ - kZ- Where k is t.docx (20)

Eigenvalues

Construction of BIBD’s Using Quadratic Residues

Ch05 1

Basic Introduction to Algebraic Geometry

machinelearning project

04_AJMS_330_21.pdf

Solutions Manual for An Introduction To Abstract Algebra With Notes To The Fu...

Proofs nearest rank

Klt

Cis435 week03

PART VII.3 - Quantum Electrodynamics

Imc2017 day1-solutions

Iterative methods

Binomial Theorem, Recursion ,Tower of Honai, relations

Lemh1a1

Number theory

Solution baupc 1999

Z transform and Properties of Z Transform

lec z-transform.ppt

More from darlened3

Lightning strike is deadly- and it happens due to the fact that Questi.docx

darlened3

Light travelling through the air (n = 1) strikes the surface of a diamond (n = 2.42) at a large angle of incidence. Which of the following describes the light ray as it enters the diamond? a) the light bends toward the normal to the surface, and slows down b) the light bends toward the normal to the surface, and speeds up c) the light bends away from the normal to the surface, and slows down d) the light bends away from the normal to the surface, and speeds up e) the light ray does not enter the diamond, but totally reflects and stays in the air Solution When light is enter into rare medium to denser medium than light rays bends towards the normal. Light slows as it travels through a substance and every substance has an index of refraction which defined as the ratio of the speed of light in vacuum to the speed of light in that substance. The index of refraction for diamond is 2.4 which means that light is 2.4 times slower in diamond . Hence Option A is correct. Hope it will help you. Please rate the answer. .

Light travelling through the air (n - 1) strikes the surface of a diam.docx

darlened3

Letâ€™s say your company doesn\'t want to upgrade from Windows Server 2008. Just focusing on the Event Viewer and the monitoring tools available in Windows Server 2012, explain to your company that how much better it is with Windows Server 2012. Solution With Windows Server 2012 R2 we can scale to run your most important workloads with robust recovery options. Weâ€™ll achieve value quickly with a wide range of cost-effective, high-performance storage options and simplified delivery of multi-tenant IT services. We can build, deploy, operate, and monitor applications on premises and in the cloud. Empower users with secure access to corporate resources on the devices they choose. Enterprise-class Improve performance and scale capacity more efficiently to run your largest workloads while enabling robust recovery options to protect against outages. Simple and cost-effective Deliver multi-tenant-aware storage and networking multi-tenancy capabilities for storage and networking on low-cost, industry-standard hardware. Application focused With enhanced support for open frameworks, we can build, deploy, and scale applications and websites with more flexibility by unlocking application portability between on-premises environments and public and service provider clouds. User-centric Deploy a virtual desktop infrastructure and lower storage costs significantly using a broad range of storage options and VHD deduplication. .

Lets say your company doesn-'t want to upgrade from Windows Server 200.docx

darlened3

Let\'s shift our focus a little and talk about Telehealth. Using to resources and APA citations: What is it and what are some different career opportunities for nurses using telehealth (e.g., nurse-run call centers for insurance companies). How is privacy maintained? Solution Telehealth Technologies -- Offering a wide array of new opportunities for nurses worldwide The good news about telehealth is that not only can it be of great value to patients in remote locations, it can also help nurses in their everyday practice and provide them with an expanded set of career choices. Telehealth makes it possible to share medical skills, information, and know how; it can also provide nurses -- be they novices, experts, or somewhere in-between -- the opportunity to play an important role in the development, deployment, and utilization of telemedicine and telehealth applications in patient care. Telehealth technologies allow clinicians to conduct remote physical assessment and consults, as well as capture and store patient information (with a store-and-forward software application) for further evaluation and sharing with a consulting physician or nurse practitioner. Telehealth/Telemedicine/e-Health - What\'s Important to Know There are six areas that are important to master in clinical telemedicine. Resources Nurses can educate themselves on these areas in several ways, including: .

Let-'s shift our focus a little and talk about Telehealth- Using to re.docx

darlened3

Let L(x1; x2; x3; x4; x5; x6; x7) = 2x3 + 3x4 + 8x6 + x7: Is L a linear map? If it is, find as many independent vectors in Ker(L) as you can. Solution L(x1; x2; x3; x4; x5; x6; x7) = 2x3 + 3x4 + 8x6 + x7 Since L satisfies scalar multipication and addition properties, it is a LINEAR map rank of transformation matrix = 4 =>dimension of kernal = 7-4 = 3 =>maximum number of independent vectors in kernel = 3 =>these vectors are : (1 0 0 0 0 0 0), ( 0 1 0 0 0 0 0) , (0 0 0 0 1 0 0 ) .

Let L(x1- x2- x3- x4- x5- x6- x7) - 2x3 + 3x4 + 8x6 + x7- Is L a linea.docx

darlened3

Solution Answer The reverse reaction cannot occur Explanation Reverse reaction is nonspontaneous: True statement because potential energy of CO2 + H2O is lower than Potential energy of Butane +O2 Butane and Oxygen have greater potential energy than CO2 + H2O : True statement Ther forward spontaneous reaction occurs once the activation energy provided : true statement The reverse reaction cannot occur : not correct because reverse reaction can be achieved in different path way. .

Look at the energy curve for butane and oxygen combining to form CO2.docx

darlened3

List regional priority credits available for Long Island. Do you think regional difference should be included in sustainable development - if yes, why - if not, why not? Solution The following are some of the regional priorties for long islands 1.SGRID3 2.Broad hollow bioscience facility 3.winthrop University Hospital 4.stony brook center for biomedicine 5.business investments 6.ronkonkoma hub 7.wyandanch rising 8.wincoram Commons 9.nassau hub 10.hempstead village 11.meadows at yaphank 12.brookhaven rail terminal 13.sheltair 14.commercial fishing infrastructure improvements 15.STEM(science , technology, engineering, m mathematics education) Yes because the aim of sustainable development is to define viable schemes combining the economic, social, environment aspects of human activity. these three areas must therefore be taken into consideration by communities companies and individuals Sustainable development implies the fulfillment of several conditions: preserving the overall Balance, respect for the environment, preventing the exertion of natural resources. reduced production of waste and the rationalitation of production and energy consumption must also be implemented. this development is differece regional difference .

List regional priority credits available for Long Island- Do you think.docx

darlened3

List the most common arguments and describe the effect of that argument of the utilities below: 7-zip Gzip Rar Tar Zip Solution 1) 7-zip : The 7-zip is an open source. it makes easy to obtain and use. it has main features like high compression ration in 7z format. -Self extraction capabalities for 7z format.Extra features include password protection as well as adjustable compression levels, compatibility with multiple archive formats.It aslo provides command line and Graphical user interface. Most common arguments and effects : Command Line (non-switch) 2) g-zip :it is a compression utility designed to be a replacement for compress.Basically it find matching strings throughout the file and replaces them to reduce the file size. Most common arguments and effects : Command-Line : 3) Rar :it is used to compress the media content that has to be shared over the internet.Files can be divided into multriple segments for compression. Further abilities include error recovery. and it supports file spanning. Most common arguments and effects : Archive compression Ratio 4) Tar : A TAR file is an archive file that contains one or more files inside. This is often done to ease distribution of a large set of files over the Internet.Â Â Its initial purpose was to backup data to sequential I/O devices. Cpmmand Line arguments : 5) Zip : it is a popular format widely used in internet. Like other archives Zip files are data containers,they store one or several files in compressed format. .

List the most common arguments and describe the effect of that argumen.docx

darlened3

Listed below are current asset items for Lester Company at December 31.docx

darlened3

List some ways in which the privacy threats posed by cyber technology differ from those posed by earlier technologies. Solution For the privacy threats posed by cyber technology there are such as the private sector carries significant responsibility for cyber security.It more like of the information generated Threats are moving to the mobile sphere Recently the International Cyber Security Protection Alliance (ICSPA) released a cyber-crime study that highlighted mobile communications Second more important thing is Privacy protection and cyber security should be thought of as interconnected: as more and more personal information is processed or stored online, The privacy protection increasingly relies on effective cyber security. This is implementation by organizations to secure personal data both when it is in transit and at rest The main reason is the Complexity of the connected environment.Through this environment only the secuirity breaks most of the time se Data risk is also comes under cyber secuirity risk For stop this secuirity violation cyber secuirity policy needs to improve by there cloud , server connection, network .

List some ways in which the privacy threats posed by cyber technology.docx

darlened3

List three factors that contribute to the severity of acid rock drainage at Earth\'s surface, such as from legacy coal mining. Solution Acid rock drainage is formed by the natural oxidation of common sulphitde minerals when they are exposed to water & aIR FACTORS THAT CONTRIBUTE TO THE SEVERITY OF ACID ROCK DRAINAGE (ARD)AT EARTH SURFACE ARE Temperature: Pyrite oxidation occurs most quickly at a temperature around 30Â°C. Microorganisms present: Some microorganisms are able to accelerate ARD production. Amount of oxygen present: Sulphide minerals oxidize more quickly where there is more oxygen available. As a result, ARD formation rates are higher where the sulphides are exposed to air than where they are buried under soil or water .Amount of water available: Cycles of wetting and drying accelerate ARD formation by dissolving and removing oxidation products, leaving a fresh mineral surface for oxidation. In addition, greater volumes of ARD are often produced in wetter areas where there is more water available for reaction. Type of minerals present: Not all sulphide minerals are oxidized at the same rate, and neutralization by other minerals present may occur, which would slow the production of ARD. .

List three factors that contribute to the severity of acid rock draina.docx

darlened3

List the GL entries (debit and credit) for the following items - list debit/credit by date for each date listed. On January 2, 2015, an agency decides to order $2,000 of office supplies. The agency has made firm orders for specific vendors. The amounts total $2,000. There are no advances. What is the GL entry when the agency signs the order (but has not yet received the supplies), On February 2, 2015, the agency receives the goods â€“ the goods are considered expenses, and are not considered personal or real property (or inventory). What is the GL entry? On February 17, 2015, the vendor receives payment for the goods. How did the vendor (likely) receive payment? Who actually paid the vendor, in most cases? What is the GL entry? Solution Answer: 2 jan 2015 Office supplies A/C Dr. $2000 To Account Payables A/CÂ Â Â $2000 2 Feb 2015Â Â Office supplies Expense A/C dr.$2000 To office supplies A/CÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â $2000 17 Feb 2015Â Â Â Â Â Accounts Payable A/C Dr. $2000 To cash A/CÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â $ 2000 Vendor receive the payment in cash. Agency actually paid the vendor. .

List the GL entries (debit and credit) for the following items - list.docx

darlened3

list examples of the internet entities( switches, web servers, mail server, users and system) need to communicate securely? Solution ARPANET was designed to support the interconnection of networks ( inter-networking ). Routers connect the various individual networks and links together that make up the Internet. switch is a computer networking device that connects devices together on a computer network, firewall is a combination of hardware and software that isolates an organizationâ€™s internal network from the Internet at large, allowing some packets to pass and block- ing others. A web server is an information technology that processes requests via HTTP, the basic network protocol used to distribute information on the World Wide Web. users navigate from one web page to another via hyperlinks embedded in the documents. These documents may also contain any combination of computer data, 1) User end system (customer) and web server (online store) in business transactions 2) User end system (laptop) and a password protected router (Wi-Fi internet) during log on 3) Two web servers (email service) in sending an email .

list examples of the internet entities( switches- web servers- mail se.docx

darlened3

List and define the factors that are important to successful implementation efforts. List and define the factors that are important to successful implementation efforts. Solution Q)List and define the factors that are important to successful implementation efforts. Ans) Several factors are important to the successful implementation of a system: including 1. management support, 2. The involvement of users, and 3. User expectations. Additionally, 4. commitment to the project, 5. commitment to change, and 6. extent of project definition and planning are important. Commitment to the project refers to managing the project so that the problem being solved is well understood and the target system actually solves the problem. Commitment to change means being willing to change behaviors and procedures. The premise of project definition and planning is that more extensive planning is more effective than less extensive planning. .

List and define the factors that are important to successful implement.docx

darlened3

List some places that may be using Network Address Translation (NAT) and how do they use it. Solution In this way Network Address Translation (NAT) is mainly working through LAN and WirelessLAN to be mapped in a single public IP address. Communicate with multiple devices on network structure is designed for easiest manner. In NAT is network designed for inside and outside network. NATs are widely used in Wi-Fi zones and UWLAN, WAN technologies and it translate private address and legal address into single layer. Metropolitan cities are using in this technology because single port but multiple access Space communication also using NAT, easily packet transmission into two or more communication channels in different categories. Military service is used in various aspects, message (packet) transfer in one IP address through entire communication channel. Civil democratic living areas are mobilized in easy to connects and configure their network channels in own arrangements. .

List some places that may be using Network Address Translation (NAT) a.docx

darlened3

List Five differences in the Format of Foreign vs Domestic Companies Income Statement. List Five differences in the Format of Foreign vs Domestic Companies Balance Sheet. Solution Differences between IFRS and U.S. GAAP Issue IFRS U.S. GAAP Documents included in the financial statements Balance sheet Income statement Changes in equity Cash flow statement Footnotes Balance sheet Income statement Statement of comprehensive income Changes in equity Cash flow statement Footnotes Balance sheet Requires separation of current and noncurrent assets and liabilities Recommends separation of current and noncurrent assets and liabilities Deferred taxes Shown as separate line items on the balance sheet Included with assets and liabilities Minority interests (usually ownership positions by significant but not majority investors) Included in equity as a separate line item Included in liabilities as a separate line item Extraordinary items (events that don .

List Five differences in the Format of Foreign vs Domestic Companies I.docx

darlened3

List and define the types of System Software. How does System Software differ from Applications Software? Solution Answer for Question: System Software Definition: System software is a type of computer program that is designed to run a computer\'s hardware and application programs. If we think of the computer system as a layered model, the system software is the interface between the hardware and user applications. Differences Between Application and System Software: Application Software: 1. Application software is computer software designed to help the user to perform specific tasks. 2. It is specific purpose software. 3. Classification: Package Program, Customized Program 4. Application Software performs in a environment which created by System/Operating System System Software: 1. System software is computer software designed to operate the computer hardware and to provide a platform for running application software. 2. System Software Create his own environment to run itself and run other application. 3. It is general-purpose software. 4. Classification: Time Sharing, Resource Sharing, Client Server Batch Processing Operating System Real time Operating System Multi-processing Operating System Multi-programming Operating System Distributed Operating System .

List and define the types of System Software- How does System Software.docx

darlened3

List and define the types of System Software. How does System Software differ from Applications Software? Solution System software are set of instructions which are used to run computer hardware and applications. It is like a bridge between hardware and user applications. System software are of threee types. 1) OPERATING SYSTEM It is designed to run process and act as a bridge between applications and user. Different Types are: * General purpose operating system * batch processing operating system * single use operating system * multi use operating system * multi programming/multi tasking operating system * multi thread operating system * Real time operating system * Embedded operating system 2) Language translator : which helps to translate high level language to assembly language. Types are: * Compiler * Interpreter * Assembler 3) Utility software: helps to organize, configure and opttimise the applications in a computer. Examples are: anti-virus software, back-up software These all are to give boost to application softwares... using these softwares.. applications run smoothly. .

List and define the types of System Software- How does System Software (1).docx

darlened3

List 6 reasons “WHY” we treat wastewater focused on the different types of contaminants in municipal wastewater. Solution Due the fact that waste water is generated with different types contaminents which are composed of salts,ammonia,pathogenic material,pesticides,chemicals such as nitrates,posphorus etc..................... Most conventional waste water plants are through rivers,lakes and streams all these plants have (National POllutant Discharges Elimination System) NPDES Different types of pollutants are present in waste water are 1) BOD (Bio Chemical Oxygen Demand) 2) Ph value 3) Total suspended values 4) coliform bacteria 5) metals 6) Total dissolved solids 7) pesticides 8) Pharacetimals The Different reasons why we treat waste water treatment focused on contaminents are 1) Clean water is critical to plants and animals that live in water and drink water This is important for fishing industries,animal lifes and plants 2) All the water that is diposed into lakes and rivers used in villages for drinking so we should treat the water for removing pollutants 3) Sewage or waste water can be recycled and used for any purpose of usage of water 4) As if we dont properly treat waste water it carries so many harmful bacteria and viruses which may cause danger to health as we play and stay with water for long time (example : oceans,rivers ) 5) The chemicals and toxic acids present in water may cause various side effects to species (any species) 6) If water is not teated all the water is sent into oceans and rivers which pollute them and cause effect to aquatic and wild life 7) If the waste water is sent into lakes or ponds all the ground water in that area is polluted So we should treate waste water depending on the contaminents present in water .

List 6 reasons WHY we treat wastewater focused on the different types.docx

darlened3

Linux distributions are becoming more and more user friendly. There is a relatively new distribution called Ubuntu that is extremely easy to install and is very functional. What additional Linux distributions are currently available, and what are their advantages and/or disadvantages? Solution The various linux distributions available are given below: 1) Finnix, its used for system administration and also comes in market with various architectures 2) Raspbian, its a a type of desktop bases distribution, its also known as a very less power computer 3) 64 Studio, its for the production of audio and video on x86 environment. 4) Corel Linux, its also one of the linux distribution. 5) Dream Linux, its one of the old linux distribution Advantages of Linux Distributions: 1) One of the advantages is that, most of the distributions of the linux are free to use and it also can be installed without license in any numbers of Computers. 2) They are more secure than windows systems, with less virus attacks 3) Opne sources and you can free to do the modifications on it. 4) Various software available to use on these distributions. 5) Robust and fast in execution. Disadvantages of Linux Distributions: 1) To understand linux distribution, you have to be patience, as its not easy as windows, to get familiar with it. 2) Not have a very strong GUI as windows. 3) Linux distributions also having various compatibility issues with other systems. 4) In terms of various applications, linux distributions are still lagging behind the windows .

Linux distributions are becoming more and more user friendly- There is.docx

darlened3

More from darlened3 (20)