Discrete mathematics / B.S. Vatsa, Suchi Vatsa.

Format:

Book

Author/Creator:

Vatsa, B. S.

Contributor:

Vatsa, Suchi.

Language:

English

Subjects (All):

Computer science--Mathematics.

Computer science.

Mathematics.

Physical Description:

1 online resource (315 p.)

Edition:

4th rev. ed.

Place of Publication:

New Delhi : New Age International, c2009.

Language Note:

English

Summary:

About the Book: The fourth edition retains all chapters of third edition and chapter 4: Ordered Sets and Lattices and chapter 10: Combinatorics as well as several sections on Set Theory, Boolean Algebra, Geometric Linear Transformation and Linear Equation are added. We have tried to emphasize that concept and terminology should be introduced before they are used. So it is useful in computer science, electrical engineering, mathematics, and professional courses also. Discrete mathematics is a pre-requisite in most computer programmes, MCA, M.Sc., B.Tech., B.Sc., BCA, BBA, PGDCA etc. of Indian Universities. A special care has been taken to make the concept of the subject and theorem on it clear by numerical illustrations so that the reader can go into the depth of the subject and make its application where he needs. Contents: Mathematical Logic Set Theory Ordered Sets and Lattices Relation and Functions Boolean Algebra and Switching Circuits Matrices Rank and Equivalence Linear Equation Characteristic Roots and Vector of a Matrix Combinatorics

Contents:

""Cover""; ""Preface to the Fourth Edition ""; ""Contents ""; ""Chapter 1. Mathematical Logic""; ""1.1 Logical Statement or Proposition ""; ""1.2 Type of Propositions ""; ""1.3 The Propositional Calculus""; ""1.4 The Negation of a Proposition ""; ""1.5 Disjunction ""; ""1.6 Conjunction ""; ""Problem""; ""1.7 Tautologies and Contradictions""; ""1.8 Logical Equivalence ""; ""Problem 1.3""; ""1.9 The Algebra of Propositions""; ""Problem 1.4""; ""1.10 Conditional Propositions ""; ""1.11 Converse, Inverse and Contrapositive Propositions""; ""1.12 The Negation of a Conditional Proposition""

""1.13 Biconditional Propositions""""Problem 1.5""; ""1.14 Arguments""; ""Problem 1.6""; ""Chapter 2. Set Theory""; ""2.1 Sets ""; ""2.2 Set Designation""; ""2.3 Null Sets and Unit Sets ""; ""2.4 Special Sets of Numbers ""; ""2.5 Universal Set""; ""Problem 2.1""; ""2.6 Subsets: Proper Subsets and Equal Sets ""; ""Problem 2.2""; ""2.7 Set Operations ""; ""2.8 Union Operation ""; ""2.9 Properties of Union Operations""; ""2.10 Intersection ""; ""2.11 Properties of Intersection Operation ""; ""2.12 Distributive Properties""; ""2.13 Complementation ""

""2.14 Relative Complement (or Difference of Sets)""""2.15 Properties of Complement ""; ""2.16 Properties of Difference ""; ""2.17 Symmetric Difference""; ""Problem 2.3""; ""2.18 Power Set ""; ""Problem 2.4""; ""2.19 Cartesian Prodcuts ""; ""Problem 2.5""; ""2.20 Generalized Set Theory ""; ""Problem 2.6 ""; ""Chapter 3. Relation and Functions ""; ""3.1 Relation ""; ""Problem 3.1""; ""3.2 Equivalence Relation""; ""3.3 Partition""; ""3.4 Partial Order Relation ""; ""Problem 3.2""; ""3.5 Functions (Mappings)""; ""Problem 3.3""; ""3.6 Inverse Mapping ""; ""3.7 Composition of Mappings""

""Problem 3.4""""3.8 Binary Operations ""; ""Problem 3.5""; ""3.9 Countable and Uncountable Sets ""; ""Problem 3.6""; ""Chapter 4. Ordered Sets and Lattices ""; ""4.1 Poset ""; ""4.2 Product Set and Order""; ""4.3 Hasse Diagrams of Partially Ordered Sets ""; ""4.4 Minimal and Maximal, and First and Last Point ""; ""Problem 4.1""; ""4.5 Lattices""; ""4.6 Lattices and Partially Ordered Sets ""; ""4.7 Principle of Quality ""; ""Problem 4.2""; ""4.8 Lattices as Algebraic Systems ""; ""4.9 Lattice and Order""; ""4.10 Sublattices""; ""4.11 Direct Product of Two Lattices ""

""4.12 Isomorphic Lattices""""Problem 4.3""; ""4.13 Complete Lattice ""; ""4.14 Complemented Lattices""; ""4.15 Distributive Lattice ""; ""4.16 Modular Lattices ""; ""Problem 4.4""; ""Chapter 5. Boolean Algebra and Switching Circuits ""; ""5.1 Introdcution ""; ""Problem 5.1""; ""5.2 Boolean Functions""; ""5.3 Normal Form ""; ""5.4 Fundamental Forms of Boolean/Functions ""; ""Problem 5.2 ""; ""5.5 Application to Switching Networks ""; ""Problem 5.3""; ""Chapter 6. Matrices ""; ""6.1 Revision""; ""6.2 Diagonal, Scalar, Unit and Triangular Matrix ""; ""6.3 Equal Matrices""

""6.4 The Transpose of Matrix: Symmetric and Skew Symmetric Matrix""

Notes:

Includes index.

ISBN:

1-282-45031-X

9786612450310

81-224-2506-2

OCLC:

923652228