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Unit - 1 Sets, Relation And Function

MODULE 1

Sets Relation And Function

1.1 TYPES OF SETS

1.2 Laws of set

1.3 Logic

1.4 Truth Table

1.5 Cartesian Product

1.6 Partition of set A collection of subsects of A is called a parition or quaotient set of a non – empty set A.

1.7 Matrix of Relation If A a1 a2 am

1.8 Types of Relation

1.9 Functions

1.10 Characteristic function of sets

1.11 Types of functions.

1.12 Composition of function

1.13 Countable

1.14 Uncountable

1.15 Cantor diagonal method

1.16 Cantor Power set Theorem Uncountable set

1.17 The Schroeder Bernstein theorem

1.18 Propositional logic

1.19 Composite sentences

1.20 Power sets

Unit - 2 Principles Of Mathematical Induction

Module 2

Mathematical induction

2.1 Principle of mathematical Induction

2.2 Well ordering principle for the integers

2.3 Question remainder theorem Division Algo

2.4 Euclidean theorem

2.5 Inductive property

2.6 Recursive definitions of sums and products

Unit - 3 Propositional Logic

Module 3

Propositional Logic

3.1 Propositional Logic is concerned with statements to which the truth values “true” and “false” can be assigned. The purpose is to analyse these statements either individually or in a composite manner.

3.2 Basic connectives

3.4 Propositional Equivalences

3.5 x Duality Principle

3.6 Rules of inference

3.7 Predicate Logic – Definition

3.8 Quantifiers

3.9 Problems

Unit - 4 Algebraic Structures And Morphism

Unit 4

Algebraic structure and morphism

4.1 Algebraic Set

4.2 General properties of multiplication.

4.3 Isomorphism

4.4 Automorphism

4.5 Homomorphism

4.6 Congruence Relation

4.6d Subgroup Let H be a subset of grou such that

4.7 Partially Ordered Set POSET

4.8 Coding

4.9 Group codes

4.10 Ring

4.11 Types of Rings

4.12 Ring homomorphisms and isomorphisms

4.13 Kernel of ring

4.14 Principle of Duality

Unit - 5 Graphs And Trees

MODULE 5

Graphs And Trees

5.1 Graphs

5.2 Bipartite graph

5.3 Isomorphism

5.4 Graph Colouring

5.5 Colouring a Cycle Graph

5.6 Edge Coloring

5.7 Trial Paths and circuit representation

5.8 Rooted Trees

5.9 Spanning Tree

5.10 Weighted graph

5.11 Prism Algorithm

5.12 Kruskal’s Algorithm

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