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MDU Mathematical Foundation of Computer Science - Sem I
Unit 3 : Propositional Logic(Prepositions, logical operations, Tautologies, Contradictions, Logical implication, Logical equivalence, Normal forms, Theory of Inference and deduction Predicate Calculus Predicates and quantifiers Mathematical Induction)
1. Predicates(Discrete Mathematics) Total View (749)

Propositional Function-The Concept, Quantifiers and First-Order Logic, The Universal Quantifier: ∀, The Existential Quantifier: ∃, Universal and Existential Statements-Equivalent Forms, Bound Variable, Negation of Quantified Statements, Contrapositive, Converse and Inverse for Universal Conditional Statements, Generalised Demorgan's Laws, Ambiguity-an Instance, Negations of Multiple-Qu ......
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 Published on: 03/11/14 Author: Jayant Ganguly Publisher: Sanguine Technical Publishers Pages: 30
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2. Mathematical Logic(Discrete Mathematics) Total View (752)

Introduction, Divisions of Logic, Statements, Truth Values, Ascertaining Truth Values of More General Compound Propositions, Conditional Statements (Implication), Biconditional (Biimplication), Logical Equivalence, Demorgan's Laws, Tautologies and Contradictions, Logical Equivalences-the Laws of Logic, Duality, Substitution Rules, Statement Formulas, Arguments (Revisited), Validity Test of Argumen ......
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 Published on: 03/11/14 Author: Jayant Ganguly Publisher: Sanguine Technical Publishers Pages: 48
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3. Fundamentals of Logic - II(Discrete Mathematical Structures ) Total View (389)

Let us consider the following statement: "whatever numbers a and b may be, (a+b)2 = a2+2ab+ b2''. The above statement is a proposition; but the bare formula "(a + b)2 = a2 + 2ab + b2'' alone is not, since it asserts nothing definite unless it was further told, or led to suppose, that a and b are to have all possible values, or are to have such-and-such values. The former of these is tacitly assume ......
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 Published on: 28/10/14 Author: Jayant Ganguly Publisher: Sanguine Technical Publishers Pages: 32
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4. Fundamentals of Logic - I(Discrete Mathematical Structures ) Total View (391)

Logic is the science and art that so directs the mind in the process of reasoning and subsidiary process as to enable it to attain clearness, consistency and validity in those processes. The aim of logic is to secure clearness in the definition and arrangement of our ideas and other mental images, consistency in our judgement and validity in our process of inference. So, logic is "A formal way of ......
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 Published on: 28/10/14 Author: Jayant Ganguly Publisher: Sanguine Technical Publishers Pages: 48
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5. Methods of Proofs, Quantified proposition, Rules of Inference, Normal Form(Mathematics) Total View (733)

Usually mathematical theorems are stated in the form of an implication p --> q or equivalence. Here P is called the Premises or hypothesis and q is called conclusion.
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 Published on: 08/01/14 Author: KSOU Publisher: Karnataka State Open University Pages: 10
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6. Predicate Calculus(Computer Science) Total View (333)

In this unit we describe the process of derivation by which one demonstrates that a particular formula in a valid consequence of given set of premises. The method of derivation involving predicated statement calculus and also certain additional rules which are required to deal with the formulae involving quantifiers. The rules P and T, regarding the introduction of a premise at any stage of deriva ......
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 Published on: 27/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 15
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7. Mathematical Logic(Applied Mathematics) Total View (8)

Mathematical logic or logic is the discipline that deals with the methods of reasoning. It provides rules and techniques for determining whether a given argument or mathematical proof or conclusion in a scientific theory is valid or not.
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 Published on: 27/05/15 Author: Bhishma Rao GSS Publisher: Scitech Publications India Pvt Ltd Pages: 109
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8. Mathematical Logic-II(Discrete Mathematical Structures ) Total View (372)

This chapter is a continuation of Chapter 2. Here, we present the topic of quantified statements and the methods of proof and disproof.
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 Published on: 27/06/14 Author: Chandrasekharaiah D S (DSC) Publisher: Prism Books Pvt Ltd Pages: 41
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9. Introduction of Scientific Research and Good Scientific Practices (GSP)(Clinical Nutrition and Dietetics) Total View (451)

The scientific enterprise is built on a foundation of trust. Society trusts that scientific research results are an honest and accurate reflection of a researcher's work. Researchers equally trust that their colleagues have gathered data carefully, have used appropriate analytic and statistical techniques, have reported their results accurately, and have treated the work of other researchers with ......
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 Published on: 02/12/13 Author: KSOU Publisher: Karnataka State Open University Pages: 15
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10. Fundamentals of Logic(Mathematics) Total View (733)

In this chapter, we study the structure of simple and compound statement through various logical connectives and different type of combination of statements.
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 Published on: 08/01/14 Author: KSOU Publisher: Karnataka State Open University Pages: 11
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11. Mathematical Logic(Computer Science) Total View (336)

The dictionary meaning of the term "Logic" is the Science of reasoning correctly. The rules of logic is precise meaning to mathematics statements. These rules are used to distinguish between valid and invalid mathematics arguments. Logical reasoning is used in mathematics to prove theorems, in Computer Science to verify the correctness of program and to prove theorems, in natural and physical sci ......
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 Published on: 28/10/14 Author: KSOU Publisher: Karnataka State Open University Pages: 23
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12. Flow Graphs and Path Testing(Software Testing ) Total View (460)

Flow Graphs and Path Testing, Objectives, Overview, Path Testing Basics, Steps in Path Testing, Construct Control Flow Graph, Flow Graph Representation, Control Flow Graph Representation, Graphical Representation, Differences between Flow Graphs and Control Flow Graphs, Arrive at Test Paths, Basic Concepts -Nodes, Links, and Paths, Path Selection Criteria, PathTesting Criteria, Picking Appropriate ......
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 Published on: 28/10/14 Author: Arunkumar Khannur Publisher: Sanguine Technical Publishers Pages: 31
 Price: Rs 23.25

13. Set Theory-Basics(Discrete Mathematics) Total View (750)

Introduction, Set Representation, Subsets, Cardinality of a Set, Venn Diagrams, Operations on Sets, Disjoint Sets, Power Set, Cartesian Product, Properties of Sets, Proving Set Indentities-Basic Technique, Duality, Properties of Empty Set, Countable and Uncountable Sets, Membership Table, Addition Principle, Miscellaneous Examples
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 Published on: 03/11/14 Author: Jayant Ganguly Publisher: Sanguine Technical Publishers Pages: 52
 Price: Rs 39

14. Mathematical Induction and Examples(Mathematics) Total View (744)

Aft.er going through this unit you should be able to learn the principle of Mathematical induction and establish some of the results involving a positive integer n.
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 Published on: 08/01/14 Author: KSOU Publisher: Karnataka State Open University Pages: 4
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15. Logic Based Testing(Software Testing ) Total View (461)

Logic Based Testing, Objectives, Overview, Decision Tables, Decision Tables in Functional Testing, Developing Decision Tables, Decision Tables in Structural Testing, Predicates and Relational Operators, Boolean Algebra, Test Case Design Using Boolean Algebra, Path expressions in the flow graph, Arrive at Boolean Expression of the Program Segment, Theorems and Laws of Boolean Algebra, Predicate exp ......
Title:
 Published on: 10/06/14 Author: Arunkumar Khannur Publisher: Sanguine Technical Publishers Pages: 67
 Price: Rs 50.25

16. Data Mining Functionalities and Data Cleaning(Computer Science) Total View (735)

Data mining functionalities are used to specify the kind of patterns to be found in data mining tasks. In general, data mining tasks can be classified into two categories: descriptive and predictive. Descriptive mining tasks characterize the general properties of the data in the database. Predictive mining tasks perform inference on the current data in order to make predictions.
Title:
 Published on: 10/01/14 Author: KSOU Publisher: Karnataka State Open University Pages: 15
 Price: Rs 11.25

17. Mathematical Logic(Mathematics) Total View (1813)

• Definitions - Logical Proposition - Truth value- • Simple and compound propositions - Logical connectives • Tautology and contradiction - Logical equivalence • Converse, inverse and contra positive of a given conditional • Switching circuits and Boolean polynomial
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 Published on: 28/10/14 Author: Sampangiram C S Publisher: Interlinepublishing Pages: 23
 Price: Rs 17.25

18. Data Mining Parameters(Computer Science) Total View (726)

A popular misconception about data mining is to expect that data mining systems can autonomously dig out all of the valuable knowledge that is embedded in a given large database,without human intervention or guidance. Although it may at first sound appealing to have an autonomous data mining system, in practice, such systems will uncover an overwhelmingly large set of patterns. A data-mining task ......
Title:
 Published on: 10/01/14 Author: KSOU Publisher: Karnataka State Open University Pages: 15
 Price: Rs 11.25

19. Logic Operations(Computer Science) Total View (200)

In this Unit, we have explained how to perform Arithmetic Operations on Floating-Point Numbers and their implementations In this topic, we _outline the general procedures for addition, subtraction, multiplication, and division of floating-point numbers. The rules we give apply to the single-precision IEEE standard formal. These rules specify only the major steps needed to perform the four, operati ......
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 Published on: 27/09/13 Author: KSOU Publisher: Karnataka State Open University Pages: 9
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20. Equivalence Relation(Computer Science) Total View (205)

Naturally we can now ask: Are there relations that simultaneously manifest all three properties? The answer is yes; For instance the relation is logically equivalent to on the set of propositions has all these properties. Such as a relation is an equivalence relation. For example in some programming languages .the names of variables can contain an unlimited number of characters that are checked w ......
Title:
 Published on: 28/09/13 Author: KSOU Publisher: Karnataka State Open University Pages: 13
 Price: Rs 9.75

21. Counting Principle(Computer Science) Total View (325)

Combinatorics, the study of arrangements of objects is an important part of discrete mathematics. This subject was studied as long as the seventeenth century. When combination questions arose in the study of gambling games, Enumeration, the counting of objects with certain properties, is an important part of combinatorics. We must count object to solve many different type of problems for instance. ......
Title:
 Published on: 27/08/13 Author: KSOU Publisher: Karnataka State Open University Pages: 21
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22. Deductive and Inductive Methods(Economics) Total View (1261)

Methodology refers to the logical process of discerning the truth relating to its contents and establishing cause and effect relationship, thereby to evolve scientific generalisations. There are two logical methods namely Deductive and Inductive method. To establish the cause of economic events, economists generally use both these methods of reasoning.
Title:
 Published on: 16/09/13 Author: KSOU Publisher: Karnataka State Open University Pages: 6
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23. Set Theory(Discrete Mathematical Structures ) Total View (390)

In our day to day life, we use the word set in so many references. But, what are sets? Well, nobody could successfully define the term set. Who ever tried, could not stop from using synonyms as "class'', "collection'', and "aggregate''. Often sets are defined intuitively as an unordered collection of objects. But this definition does not specify "what an object is?'' Such definition leads to parad ......
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 Published on: 28/10/14 Author: Jayant Ganguly Publisher: Sanguine Technical Publishers Pages: 58
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24. Theories, Models, Schools and Systems(Psychology) Total View (206)

This unit introduces the meaning and definitions of certain commonly used scientific terms.Irrespective of the branch of science, the discussed terms introduced in this unit are used with specific meaning and intention. Laymen understand and use of the same words in an almost different sense. Therefore, students of science must first become familiar with these terms before starting their study in ......
Title:
 Published on: 20/03/14 Author: KSOU Publisher: Karnataka State Open University Pages: 17
 Price: Rs 12.75

25. Domain Testing(Software Testing ) Total View (458)

Domain Testing, Objectives, Overview, Domains and Paths, Meaning of Domain Testing Model, Concepts of Domain, Open and Closed Domains, A Domain is a set, Open and Closed Domain, Domains, Paths, and Predicates, Nice Domains and Ugly Domains, Nice Domains, Ugly Domains, Domain Testing, Boundary Value Analysis, Equivalent Partitioning, Boundary Value Analysis Vs. Equivalent Partitioning Test Designs, ......
Title:
 Published on: 10/06/14 Author: Arunkumar Khannur Publisher: Sanguine Technical Publishers Pages: 22
 Price: Rs 16.5