MA2265 Discrete Mathematics Hand Written Lecture Notes - Deepthi Edition

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Discrete Mathematics (All Units) Handwritten Premium Lecture Notes, Prepared by Deepthi. Specially for Engineering Candidates. Syllabus Covered based on Anna University  B.Tech IT, R2008 and R2013 Regulation.

CONTENT:

UNIT-1 LOGIC AND PROOFS (No.of.pg:34)
UNIT-2 COMBINATIONS (No. of Pg:20)
UNIT-3 GRAPHS (No. of pg:34)
UNIT-4 ALGEBRIC STRUCTURE (No. of. Pg: 25)
UNIT-5 LATTICES AND BOOLEAN ALGRBRA (No .of .pg:20)

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UNIT-1
LOGIC AND PROOFS
Definition: proposition
Atomic IC statements
Molecular statement
Truth table
Negation or not
Conjuction
Conditional statement
Bi conditional statement
Contrapositive
Translating sentence into logical expression or symbolic form
Tautology
Contradiction
Fallacy
Duality
Disjunction
Conjunctive normal form
Principle conjunction normal form
Quantifiers
Rules of inference
Rules in quantifiers
1. Universal specification
2. Existential specification
3. Existential specification
4. Universal generalization
Hypothesis
Analisis
Conclusion
UNIT-2
COMBINATIONS
Principle of mathematical induction
Strong induction
Pigeonhole principle
Generalization pigeonhole principle
Extended pigeonhole principle
Linear recurence relation
Generating function
Inclusion and exclusion
UNIT-3
GRAPHS
Adjacent vertices
Simple graph
Parallel edges
Multi graph
Simple directed graph
Directed graph
Mixed graph
Loop
Weighed graph
Underlying undirected graph
Pseudo graphs
In degree
Out degree
Complete graph
N-cube
Star graph
Sub graph
Union
Representation graph and graph isomorphism
Properties of adjacency matrix
Connectivity
Path
Connected and disconnected graph
Connectedness in D.G
UNIT-4
ALGEBRAIC STRUCTURE
Binary operation
General properties of algebraic structure
1. Closure properties
2. Associativity
3. Commutativity
4. Identity
5. Element
6. Distributivity
7. Cancellation property
Semi graph
Monoid
Semi graph homomorphism
Monoid homomorphism
Sub monoid
Group
Abelian group
Properties of group
Langrange’s thm
Normal sub group
Kernel of a homomorphism
Isomorphism
Cosets
Integral domain

UNIT-5
LATTICES AND BOOLEAN ALGRBRA
Partial order relation
Poset
Totally ordered set
Well ordered
Hasse diagram or partially ordered set diagram
Lattice
Greatest lower band and upper post
Some properties of lattices
Theorems
Boolean algebra

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