Set Theory Continued
Theorem proving Techniques :
Mathematical Induction (simple and
strong),Counting with pigeonhole
principle,
What is Induction
A method of proof
It does not generate answers: it can only prove them
Three parts:
Base case(s): show i
Basic Graph Theory
Introduction to Graphs
Basic Definitions
Some Special Graphs
Bipartite Graphs
Operations on Graphs
Other Graph Representations
Graph Isomorphism
Other Types of Graphs:
Multigraphs
Directed Graphs
Directed Multigraphs
Paths and
DISCRETE MATHEMATICAL
STRUCTURES
Kumi Chauhan
Assistant Professor
Department of Computer science & Engineering
Introduction to DS
What is Discrete Mathematics?
What are the topics covered in Discrete
Mathematics?
Why Study Discrete Mathematics?
What a
Unit 3
Posets,Hasse diagram and lattices
Introduction
Partially Ordered Set
Comparability
Totally ordered set
Chain
Hasse Diagram of partially ordered sets
Isomorphic ordered set
Well ordered set
Properties of Lattices
Partially Ordered Sets
Examples
Set Theory Continued
Function : Definition, type of functions,
inverse function, composition of
functions, recursively defined functions.
Introduction
Definition 1. A function or mapping f from a
set A to a set B, denoted f : A B, is a
correspondence in
Propositional and
First-Order Logic
1
Propositional Logic
2
Propositional logic
Proposition : A proposition is classified as a declarative
sentence which is either true or false.
eg: 1) It rained yesterday.
Propositional symbols/variables: P, Q, S, . (a
MTH 201 Discrete Structures
Credits : 04(Lect, Tutorial, Lab : 4, 1, 0 )
Detailed Syllabus
UNIT-I
Set Theory : Definition, operations, data structure for disjoint sets. Function : Definition,
type of functions, inverse function, composition of functions,
Discrete Structures (MTH 201)
Assignment 1
Due Date -24/09/12 (Monday) before starting of the Lecture
Ques 1 : Prove by induction:
n
i .2i= ( n1 ) . 2n+1 +2
(a)
i=1
n
(b)
n
2
( )
i = i
i=1
3
i=1
Ques 2: Prove or give a counterexample for each of the
foll