...n ≥ 2. If xi is a Boolean variable for all 1 ≤ i ≤ n, prove that a) (x1 + x2 + ・ ・ ・ + xn) _ x1x2 ・ ・ ・ xn Assume the result for n _ k (≥ 2) and consider the case of n _ k + 1. b) (x1x2 ・ ・ ・ xn) _ x1 + x2 + ・ ・ ・ + xn Follows from part (a) by duality. 5. Let_be a Boolean algebra that is partially ordered by≤. If x, y, z ∈ _, prove that x + y ≤ z if and only if x ≤ z and y ≤ z. If x ≤ z and y ≤ z, then from Exercise 6(b) of Section 15.4 we have x + y ≤ z + z. z + z _ z. Conversely, suppose that x + y ≤ z.We find that x ≤ x + y, because x(x + y) _ x + xy _ x. Since x ≤ x + y and x + y ≤ z, we have x ≤ z, because a partial order is transitive. 6. State and prove the dual of the result in Exercise 5. Exercise 15.1, problems 1, 2, 11, 12, 14, & 15 1. Find the value of each of the following Boolean expressions if the values of the Boolean variables w, x, y, and z are 1, 1, 0, and 0, respectively. a) xy + x y = 1 b) w + xy = 1 c) wx + y + yz = 1 d) (wx + yz) + wy + (w + y)(x + y) = 1 2. Let w, x, and y be Boolean variables where the value of x is 1. For each of the following Boolean expressions, determine, if possible, the value of the expression. If you cannot determine the value of the expression, then find the number of assignments of values for w and y that will result in the value 1 for the expression. a) x + xy + w b) xy + w c) xy + xw d) xy + w 11. Simplify the following Boolean expressions. ...
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...15.1, problems 1a Find the value of each of the following Boolean expressions if the values of the Boolean variables w, x, y, and z are 1, 1, 0, and 0, respectively. xy + x y x y xy (xy) ̅ x ̅ y ̅ x ̅y ̅ (xy) ̅+x ̅y ̅ 1 0 0 1 0 1 0 1 Solution: 1 2a Let w, x, and y be Boolean variables where the value of x is 1. For each of the following Boolean expressions, determine, if possible, the value of the expression. If you cannot determine the value of the expression, then find the number of assignments of values for w and y that will result in the value 1 for the expression. a) x + xy + w x = 1 then x+xy+w = 1+1y+w = 1+(1y+w) 1+z = 1 for every Boolean value z then: if we take z = 1y+w 1+(1y+w) = 1 Solution: Yes is possible, x+xy+w = 1 4a a) Find the fundamental conjunction made up from the variables w, x, y, z, or their complements, where the value of the conjunction is 1 precisely when i) w _ x _ 0, y _ z _ 1. ii) w _ 0, x _ 1, y _ 1, z _ 0. iii) w _ 0, x _ y _ z _ 1. iv) w _ x _ y _ z _ 0. 9 Let Bn →B. If the d.n.f. of f has m fundamental conjunctions and its c.n.f. has k fundamental disjunctions, how are m, n, and k related? 12 Find the values of the Boolean variables w, x, y, z that satisfy the following system of simultaneous (Boolean) equations. x + xy _ 0 xy _ xz xy + x z + zw _ zw x+x ̅y=0→(x+x ̅ )(x+y)=0 Distributive Law of + over 1(x+y)=0...
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...15 supplementary question 5 5. Let be a Boolean algebra that is partially ordered by≤. If x, y, z ∈ B, prove that x + y ≤ z if and only if x ≤ z and y ≤ z. If x ≤ z and y ≤ z, then from Exercise 6(b) of Section 15.4 we have x + y ≤ z + z. And by the Idempotent Law we have z + z = z. Conversely, suppose that x + y ≤ z.We find that x ≤ x + y, because x(x + y) = x + xy (by the Idempotent Law) _ x (by the Absorption Law). Since x ≤ x + y and x + y ≤ z, we have x ≤ z, because a partial order is transitive. (The proof that y ≤ z follows in a similar way.) 15.1 Question 2 2. Let w, x, and y be Boolean variables where the value of x is 1. For each of the following Boolean expressions, determine, if possible, the value of the expression. If you cannot determine the value of the expression, then find the number of assignments of values for w and y that will result in the value 1 for the expression. a) x + xy + w b) xy + w c) xy + xw d) xy + w a) if w, x, and y be Boolean variables, where the value of x is 1, we need to determine the value of the expression x + xy + w and if it is not possible to find the value of the expression, then find the number of assignments of value for w and y that will result in the value 1 for the expression. Using the law of Identity in the given expression: we get x-1 + xy + w = x (1 + y) + w. Using the law of Dominance, we get x + xy+ w.= x -1+ w. Using the law of Identity, we get x+xy+w=x +w Putting x=1,we get...
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...Vol 3 Issue 2 March 2013 Impact Factor : 0.2105 ORIGINAL ARTICLE ISSN No : 2230-7850 Monthly Multidisciplinary Research Journal Indian Streams Research Journal Executive Editor Ashok Yakkaldevi Editor-in-chief H.N.Jagtap IMPACT FACTOR : 0.2105 Welcome to ISRJ RNI MAHMUL/2011/38595 ISSN No.2230-7850 Indian Streams Research Journal is a multidisciplinary research journal, published monthly in English, Hindi & Marathi Language. All research papers submitted to the journal will be double - blind peer reviewed referred by members of the editorial Board readers will include investigator in universities, research institutes government and industry with research interest in the general subjects. International Advisory Board Flávio de São Pedro Filho Federal University of Rondonia, Brazil Hasan Baktir Mohammad Hailat English Language and Literature Dept. of Mathmatical Sciences, University of South Carolina Aiken, Aiken SC Department, Kayseri Kamani Perera 29801 Regional Centre For Strategic Studies, Sri Ghayoor Abbas Chotana Lanka Department of Chemistry, Lahore Abdullah Sabbagh University of Management Sciences [ PK Engineering Studies, Sydney Janaki Sinnasamy ] Librarian, University of Malaya [ Anna Maria Constantinovici Catalina Neculai Malaysia ] AL. I. Cuza University, Romania University of Coventry, UK Romona Mihaila Spiru Haret University, Romania Delia Serbescu Spiru Haret University, Bucharest, Romania Anurag Misra DBS College, Kanpur Titus Pop Ecaterina...
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...Case study Submission details |Candidate’s Name | |Candidate ID | | |Assessor’s Name | | |Assessment Site | | |Assessment Date/s | |Date | | The Assessment Task is due on the date specified by your assessor. Any variations to this arrangement must be approved in writing by your assessor. Submit this document with any required evidence attached. See specifications below for details. Performance objective The candidate must be able to demonstrate a broad knowledge of research concepts, methods and processes. Assessment description The task is a case study with questions that assesses if the candidate has acquired the underpinning knowledge and skills required to gather, organise, analyse and present research information in the work place. Procedure 1. You have 5 minutes of reading time before you begin the test and 30 minutes to complete the case study questions. 2. You can ask your assessor if you are unsure about any questions. 3. You are to answer all of the questions in the time provided to you by your assessor. ...
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...Chapter 4: More on Logical, Information, and Text Functions Introduction Logical functions are those that involve Boolean values. The Boolean values are TRUE and FALSE. Some logical functions return a Boolean value as their result, others use the Boolean result of a comparison to choose between alternative calculations. There are six functions listed in the logical group in Excel 2003 – the functions AND, FALSE, IF, NOT, OR, TRUE – and a seventh in Excel 2007 – the function IFERROR. You’ll see the use of most of these in this lab. First, however, it’s worthwhile to become familiar with the logical operators. Logical Operators TRUE and FALSE are common concepts. They are values which pertain to statements. For example, the statement “It is morning.” is either TRUE or FALSE. We recognize that its truth value may change, but at any particular time the statement is either TRUE or FALSE. What may be hidden here is the existence of an implied comparison. To determine the truth value of any statement we compare our understanding of the meaning of the claim with the facts. Strictly speaking the statement “It is morning.” means the time of day is after midnight and before noon. To decide if it’s TRUE we need to know the actual time of day and compare it to our criteria. It’s in these comparisons that we use Logical Operators: |Comparison |Symbol | |less than |< | |less...
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...DIALOG The Dialog service is the world's most comprehensive online information Retrieval service and has been serving users since 1972. With over 600 databases from a broad range of disciplines, Dialog provides international access to information in a broad scope of subject areas. The volume of data available combined with the system's searching capabilities make Dialog the largest and most powerful online service of its type. The Dialog content collection contains hundreds of databases comprised of millions of documents drawn from a multitude of sources. Dialog brings you scientific and technical literature; full-text trade journals, newspapers and newswires; details on millions of chemical substances; information on patents and trademarks issued worldwide; demographic data; and company financial statistics. Accessing Dialog. All Dialog Command Language interfaces are accessible via the Internet using TCP/IP protocols, most commonly using: A Web browser. Internet Explorer 5.X or higher or Netscape Navigator 4.7 or higher are recommended. Internet access is available at the desktop in most businesses and academic institutions. Internet Service Providers (ISP) also provides Internet access for a fee by means of a telephone dial-up connection, DSL broadband cable, or wireless service. In addition to Internet access, you will also need a valid user account for Dialog. Each account is assigned User ID and password that are required in order to log on to the service. Institutions...
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...Computer Science Chapter 1: Introduction to Computer Hardware Different Categories of Computer and Computing Devices Tablets The lightest and most portable Touch interface, good for “light” work Laptops/Notebooks Larger display area; adds CD or DVD as well as physical keyboard They are portable; price for performance is not as good as desktop, choice of hardware is limited Specialized Variant Laptops Ultrabooks Thinner, and lighter than laptops Cost is higher than laptop (all hardware being equal) Netbooks Cheaper more portable laptop that is smaller and has a lower quality display and overall less powerful hardware Much less common than tablets today Desktop Computers Everything is separate (monitor, computer, keyboard, etc); this allows you to mix and match and customize your desktop computer, at the cost of increased complexity (some compatibility issues may arise – not everything works together) and decreased portability. Larger ‘footprint’ (More space is required, but this allows for increase expandability) ------------------------------------------------- Reduced costs/more options (compared to laptops) ------------------------------------------------- The purpose of an operating system is to run the computer. The operating system determines the interface of a computer, its configurability, and its security. In general, due to popularity and tweak-ability, the MS-WINDOWS (PC) OS has more viruses than the MAC OS. In general, the MAC OS...
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...so if the vice president, and the secretary voted yes, but the president and treasurer voted no, since the president's vote is a no, the majority vote would end with a no vote. we had to create a truth table of every different outcome to make sure everything would check out. then after that we would get all of the ones with a positive outcome, and then write them all out as if it were a math problem. then using this stuff called boolean algebra, we had to make the bigger math problem much simpler so it would fit into the circuit system that we use to simulate how it would look in real life. the simplification was very long and quite difficult. it is very confusing and very difficult to explain. so to simplify it, the example i'm going to give you is very simple compared to what we had to do. so say that the president said no, so in the simplification, it would be not P, or not president. and continuing this same process down the line until you would get them all. say that two terms would be PT and the others would be P and not T, according to boolean you could just write it as P(T+not T) and it would be the same while eliminating a gate, which is what we would use to wire these up. when you would wire them up a + sign is an or gate. which takes two inputs and says if one of these are on and the other is off, it will go through as on. and a X would be an and gate, those will only pass the signal if both inputs are the same....
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...1. what is e-classroom? 2. what is industrial robot? Explain that. 3. Describe about the process that Mubin told about his parents. 4. ICT used for doing many dangerous situation succesfully. Explain that. Answers: 1. main book. 2. Industrial robot is a robot that is used in many dangerous work. Now all the industrial work in industry are done by industrial robot. Human become tired,bored but robot never. Robot can do work for long time. In the big industry of the world now robot is uses as labor. 3. Mubin told his parents about the use of computer in operating phone. He also told about the drone system. Mubin works in air force thats why his parents always anxious for him.They think about the airplane accident. Then mubin told them about the latest technology that used in aircraft. Now all the airplane are opetated by computer. Now pilot dont have to do many things. So the posibility of the plane accident now become less. Now a days there is no pilot in the fighter plane. The drone system is used normally in war. 4. Besides the use in aircraft ICT also used in many dangerous sector for doing many dangerous work. Now most of the work in the big industry is done by robot bacuase robot dont get tired or bored like human. Now human just observe the work either its right or wrong. Now in transportation the use of ICT increased a lot. In future if car dmis driven by robot then the number of road accidents will definately less. So now ICT is used in many dangerous sector...
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...Use of Information Search Techniques and Tools on Web By Prof. A. B. Bhosle* A university, a college or an institution of higher learning is rightly described as community where teachers and scholars are the head, students are the body and the library is it’s heart. If the body is to perform its function properly and efficiently its hearth must be well maintained and strong in its functioning. Thomas Carlyle was not exaggerating when he described a ‘true university as a collection of books’.[1] The library is obviously the source of power of knowledge. In higher education and research, the use of library is a matter of concerns to students, teachers, and researchers. The exponential growth of literature often creates problems for them to access appropriate literature and their use. The problem has, however, considerably been resolved with the help of information and communication technology (ICT). The use of information technology for management and handling of information and data has grown significantly even in many least-developed countries, despite their economic constraints. The use of information technology in libraries has been profoundly affecting all aspects of information acquisition, storage, and transfer. Its magnificent development has dramatically changed the mode of library operations and information services; we have now started to speak of a new type of information source, ‘knowledge base’.[2] Computer-based communications have not only widened...
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...Final Exam Review 1. Topics to study a) Chapter 2 – Fundamentals of Logic b) Chapter 3 – Set Theory c) Chapter 4 – Induction and the Division Algorithm d) Chapter 5 & 7 – Relations and Functions e) Chapter 1 – Combinatorics f) Chapter 8 – Inclusion/Exclusion Principle 2. Chapter 2 – Fundamentals of Logic a) Logical Connectives i) Conjunction ii) Disjunction iii) Negation iv) XOR v) Implication vi) Bi-Direction b) Truth Table construction 8. Construct a truth table for each of the following compound statements, where p, q, r denote primitive statements. Tell whether the given statement is a tautology. a. ¬ (p Ú ¬q) → ¬p p q ¬q ¬p p Ú ¬q ¬ (p Ú ¬q) ¬ (p Ú ¬q) → ¬p 0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 The statement is a tautology. b. p → (q → r) p q r q → r p → (q → r) 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 The statement is not a tautology. c. (p → q) → r p q r p → q (p → q) → r 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 The statement is not a tautology. d. (p → q) → (q → p) p q p → q q → p (p → q) → (q → p) 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 The statement is not a tautology. e. (p (p → q)) → q p q p → q p (p → q) (p (p → q)) → q 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 The statement is a tautology. f. (p q) → p p q p q (p q) → p 0 0 0 1 0 1 0 1 1...
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...To: From: cc: Subject: Date: This memo describes the progress on the Computer Recycling Work Station (CRWS) project. We are to design a way for the CRWS to be effective and efficient to allow workers to safely test and disassemble used computers or used computer components and allocate them into three different routes: scrap, recycle, or resale Progress: Our first step was to develop an IDEF0 of the computer disassembly process in which the CRWS will be designed to operate all necessary steps and requirement. The IDEF0 modeling language displays multiple interactions between processes and elements of complex systems. The model that was developed was created form the viewpoint of Industrial Engineers using logical understanding of how to assemble or disassemble computers. Our attached document shows our model containing A-0, A0, A1, A2, and A3 level. At A-0 level a single task of disassembling a used computer is presented with resale, scrap, and recycle as the desired outputs. At A0 level contains three separate steps in the process: A1 (test computer), A2 (disassemble computer), and A3 (test component). Those three separate steps have their own detailed processes with the same outputs. Requirements: Using the program to help make the IDEF0 diagram look more professional, we have expanded each process in the A0 level to display the logical steps involved in disassembling the computer and its components by putting it together into an attached document...
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...Distributed System and Centralized Failures By Kentrell Lanier POS/355 March 28, 2014 Paul Borkowski Distributed System and Centralized System Failures Distributed system is many computers linked together that take on different tasks and act like one big computer. Distributed system is found in business across the world. When computers are linked together they share the same database and server. Distributed system is constructed for resource sharing, computation speedup, reliability, and communication Distributed system have different names for the computers in the system. Names such as sites, nodes, computers, machines, and host. Each names goes to a computer that’s part of the system. Resource sharing is when computers link up and they have different data any user can use the data form any computer in the system. Computation speedup is when the system recognize that one computer is over worked so the system have computers that’s have less duties to perform the tasks. Computation speedup help the system from crashing and tasks are preformed quicker. Distributed systems are more reliable because if one computer crash or fail the others can share its responsibilities and system will continue running smoothly. By computers being link together the users can communicate between each other. Two Types of failure When dealing with computers there are two types of failures. You can have a hard drive failure or a software failure. A hard drive failure is when the disk drive fails to...
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...to MEDLINE at http://www.pubmed.gov and conduct a search on your clinical question. Please type your search history in the table below: Search Number | P | I | C | O | T | # of Results | Notes | 1 | Congestive Heart Failure | | | | | 33058 | I typed “congestive heart failure” in the search field and clicked ‘Search’. | 2 | | Home Monitoring | | | | 1077 | I cleared the search field and typed in “home monitoring” and clicked ‘Search’. | 3 | | | | Decreased Readmission | | 11954 | I cleared the search and typed in readmission instead of decreased readmission to widen my search results and clicked ‘Search’. | 4 | #1 | #2 | | #3 | | 40 | I then clicked ‘Advanced Search’ and combined Searches #1, #2, and #3 using the Boolean operator “AND”. I then clicked ‘Search’. | 5 | #1 | #2 | | #3 | 5 years | 22 | I chose to further the search by retrieving only current articles, so I used the same ‘Advanced Search’ from 4 but then clicked on ‘Limits’ and requested only articles from the last 5 years. I then clicked ‘Search’. Although 10-20 articles is preferred I felt 22 returned articles was still close. | | | | | | | | | | | | | | | | | 4. Search: EBSCO/CINAHL Go to the Chamberlain Library at http://www.chamberlain.edu/library and enter EBSCO. Conduct a search on your clinical question. Please type your search history...
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