For more information about this title,click here CONTENTS CHAPTER 1 Set Theory y 1.1 Introduction 1.2 Sets and Elements,Subsets 1.3 Venn Diagrams 1.4 Set Operations 1.5 Algebra of Sets,Duality > 1.6 Finite Sets,Counting Principle P 1.7 Classes of Sets,Power Sets,Partitions 10 1.8 Mathematical Induction 12 Solved Problems 12 Supplementary Problems 18 CHAPTER 2 Relations 23 2.1 Introduction 2.2 Product Sets 2.3 Relations 2.4 Pictorial Representatives of Relations 2.5 Composition of Relations 2.6 Types of Relations 2.7 Closure Properties 2.8 Equivalence Relations 2.9 Partial Ordering Relations 334357283013460 Solved Problems Supplementary Problems CHAPTER 3 Functions and Algorithms 43 3.1 Introduction 43 3.2 Functions 43 3.3 One-to-One,Onto,and Invertible Functions 3.4 Mathematical Functions,Exponential and Logarithmic Functions 3.5 Sequences,Indexed Classes of Sets 3.6 Recursively Defined Functions 3.7 Cardinality 3.8 Algorithms and Functions 3.9 Complexity of Algorithms Solved Problems 1702567606 Supplementary Problems viiCONTENTS CHAPTER 1 Set Theory 1 1.1 Introduction 1 1.2 Sets and Elements, Subsets 1 1.3 Venn Diagrams 3 1.4 Set Operations 4 1.5 Algebra of Sets, Duality 7 1.6 Finite Sets, Counting Principle 8 1.7 Classes of Sets, Power Sets, Partitions 10 1.8 Mathematical Induction 12 Solved Problems 12 Supplementary Problems 18 CHAPTER 2 Relations 23 2.1 Introduction 23 2.2 Product Sets 23 2.3 Relations 24 2.4 Pictorial Representatives of Relations 25 2.5 Composition of Relations 27 2.6 Types of Relations 28 2.7 Closure Properties 30 2.8 Equivalence Relations 31 2.9 Partial Ordering Relations 33 Solved Problems 34 Supplementary Problems 40 CHAPTER 3 Functions and Algorithms 43 3.1 Introduction 43 3.2 Functions 43 3.3 One-to-One, Onto, and Invertible Functions 46 3.4 Mathematical Functions, Exponential and Logarithmic Functions 47 3.5 Sequences, Indexed Classes of Sets 50 3.6 Recursively Defined Functions 52 3.7 Cardinality 55 3.8 Algorithms and Functions 56 3.9 Complexity of Algorithms 57 Solved Problems 60 Supplementary Problems 66 vii For more information about this title, click here