CHAPTER 1: SET RELATION FUNCTION; 1.1 INTRODUCTION; 1.2 SETS; 1.2.1 Representation of a Set; 1.2.2 Sets of Special Status; 1.2.3 Universal Set and Empty Set; 1.2.4 Subsets; 1.2.5 Power set; 1.2.6 Cardinality of a Set; 1.3 ORDERED PAIRS; 1.3.1 Cartesian Product of Sets; 1.3.2 Properties of Cartesian Product; 1.4 VENN DIAGRAMS; 1.5 OPERATIONS ON SETS; 1.5.1 Union of Sets; 1.5.2 Intersections of Set; 1.5.3 Complements; 1.5.4 Symmetric Difference; 1.6 COUNTABLE AND UNCOUNTABLE SETS; 1.7 ALGEBRA OF SETS; 1.8 MULTISET; 1.8.1 Operations on Multisets; 1.9 FUZZY SET; 1.9.1 Operations on Fuzzy Set; 1.10 GROWTH OF FUNCTION; 1.11 COMPUTER REPRESENTATION OF SETS; 1.12 INTRODUCTION; 1.13 BINARY RELATION; 1.14 CLASSIFICATION OF RELATIONS; 1.14.1 Reflexive Relation; 1.14.2 Symmetric Relation; 1.14.3 Antisymmetric Relation; 1.14.4 Transitive Relation; 1.14.5 Equivalence Relation; 1.14.6 Associative Relation; 1.15 COMPOSITION OF RELATIONS; 1.16 INVERSE OF A RELATION; 1.17 REPRESENTATION OF RELATIONS ON A SET; 1.18 CLOSURE OPERATION ON RELATIONS; 1.18.1 Reflexive Closure; 1.18.2 Symmetric Closure; 1.19 MATRIX REPRESENTATION OF RELATION; 1.20 DIGRAPHS; 1.20.1 Transitive Closure; 1.20.2 Warshall's Algorithm; 1.21 PARTIAL ORDERING RELATION; 1.22 n-ARY RELATIONS AND THEIR APPLICATIONS; 1.23 RELATIONAL MODEL FOR DATABASES; 1.24 INTRODUCTION; 1.25 ADDITION AND MULTIPLICATION OF FUNCTIONS; 1.26 CLASSIFICATION OF FUNCTIONS; 1.26.1 One-to-one (Injective) Function; 1.26.2 Onto (Surjective) Functions; 1.26.3 One-to-one, Onto (Bijective) Function; 1.26.4 Identity Function; 1.26.5 Constant Function; 1.27 COMPOSITION OF FUNCTION; 1.27.1 Associativity of Composition of Functions; 1.28 INVERSE FUNCTION; 1.28.1 Invertible Function; 1.28.2 Image of a Subset; 1.29 HASH FUNCTION; 1.30 RECURSIVELY DEFINED FUNCTIONS; 1.31 SOME SPECIAL FUNCTIONS; 1.31.1 Floor and Ceiling Functions; 1.31.2 Integer and Absolute Value Functions; 1.31.3 Remainder Function; 1.32 FUNCTIONS OF COMPUTER SCIENCE; 1.32.1 Partial and Total Functions; 1.32.2 Primitive Recursive Function; 1.32.3 Ackermann Function; 1.33 THE INCLUSION-EXCLUSION PRINCIPLE; 1.33.1 Applications of Inclusion - Exclusion Principle; 1.34 SEQUENCE AND SUMMATION; 1.34.1 Sequence; 1.34.2 Summation; SUMMARY; EXERCISE 1; CHAPTER 2 COMBINATORICS; 2.1 INTRODUCTION; 2.2 BASIC PRINCIPLES OF COUNTING; 2.2.1 Multiplication Principle (The Principles of Sequential Counting); 2.2.2 Addition Rule ( The Principle of Disjunctive Counting); 2.3 FACTORIAL NOTATION; 2.4 BINOMIAL THEOREM; 2.4.1 Pascal's Triangle; 2.4.2 Multinomial Theorem; 2.5 PERMUTATIONS (Arrangements of Objects); 2.5.1 Permutations with Repetitions; 2.5.2 Circular Permutations; 2.6 COMBINATIONS (Selection of Objects); 2.6.1 Combinations of n Different Objects; 2.6.2 Combinations with Repetitions; 2.7 DISCRETE PROBABILITY; 2.7.1 Terminology (Basic Concepts); 2.8 FINITE PROBABILITY SPACES; 2.9 PROBABILITY OF AN EVENT; 2.9.1 Axioms of Probability; 2.9.2 Odds in favour and Odds against an Event; 2.9.3. Addition Principle; 2.10 CONDITIONAL PROBABILITY; 2.10.1 Multiplication Rule; 2.11 INDEPENDENT REPEATED TRIALS, BINOMIAL DISTRIBUTION; 2.11.1 Repeated Trials with Two Outcomes, Bernoulli Trials; 2.12 RANDOM VARIABLES; 2.12.1 Probability Distribution of a Random Variable; 2.12.2 Expectation of a Random Variable; 2.12.3 Variance and Standard Deviation of a Random Variable; 2.12.4 Binomial Distribution; 2.13 RECURSION; 2.13.1 Recursively Defined Sequences; 2.13.2 Recursive Definitions; 2.13.3 Recursively Defined Sets; 2.13.4 Recursively Defined Functions; 2.14 RECURENCE RELATION; 2.14.1 Order and Degree of Recurrence Relation; 2.14.2 Linear Homogenous and Non-homogeneous Recurrence Relations; 2.14.3 Solution of Linear Recurrence Relation with Constant Coefficients; 2.14.4 Homogenous Solution; 2.14.5 Particular Solution; 2.15 GENERATING FUNCTIONS; 2.16 COUNTING (COMBINATORIAL) METHOD; 2.17 THE PIGEONHOLE PRINCPLE; 2.17.1 Generalized Pigeonhole Principle; SUMMARY; EXERCISE 2;