Discrete Mathematics (MA3354) - Anna University
Course Instructor
Promath
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Course Overview
Schedule of Classes
Course Curriculum
6 Subjects
Unit - I : Logic and Proofs
97 Learning Materials
1.1 Basic of Logic
1.1.1 Introduction of discrete mathematics
PDF
1.1.2 Introductionof basic of logic
PDF
1.1.3 Proposition and connectives
PDF
1.1.4 Five basic connectives
PDF
1.1.5 Statement formula
PDF
1.1.6 Solved problem 1
Video
2:31
1.1.7 Solved problem 2
Video
4:12
1.1.8 Solved problem 3
Video
3:8
1.1.9 Solved problem 4
Video
3:7
1.1.10 Solved problem 5
Video
3:41
1.1.11 Solved problem 6
Video
4:53
1.1.12 Solved problem 7
Video
5:00
1.1.13 Solved problem 8
Video
4:33
1.2 Tautology
1.2.1 Tautology
PDF
1.2.2 Solved problem 1
Video
4:12
1.2.3 Solved problem 2
Video
5:30
1.2.4 Solved problem 3
PDF
1.2.5 Solved problem 4
PDF
1.2.6 Solved problem 5
PDF
1.2.7 Equivalence of formulas
PDF
1.2.8 Solved problem 1
Video
4:12
1.2.9 Solved problem 2
Video
6:37
1.2.10 Solved problem 3
Video
4:2
1.2.11 Solved problem 4
PDF
1.2.12 Solved problem 5
PDF
1.2.13 Tautology Implications
PDF
1.2.14 Solved problem 1
Video
3:39
1.3 Converse, Contrapositive And Inverse Propositions
1.3.1 Converse, Contrapositive And Inverse Propositions
PDF
1.3.2 Solved problem 1
Video
2:43
1.3.3 Solved problem 2
Video
2:30
1.3.4 Solved problem 3
Video
2:41
1.3.5 Solved problem 4
Video
6:26
1.3.6 Functionally complete set
PDF
1.3.7 Examples
PDF
1.4 Normal Form
1.4.1 Normal Form
PDF
1.4.2 Implication Rules
PDF
1.4.3 Disjunctive normal form (DNF)& Conjunctive normal form(CNF)
PDF
1.4.4 Solved problem 1&2
PDF
1.4.5 Solved problem 3
Video
6:30
1.4.6 Solved problem 4
Video
8:21
1.4.7 Solved problem 5
Video
6:5
1.4.8 Solved problem 6
PDF
1.5 principal normal forms
1.5.1 Minterms & Maxterms
PDF
1.5.2 PDNF & PCNF
PDF
1.5.3 Solved problem 1
Video
6:34
1.5.4 Solved problem 2
Video
5:23
1.5.5 Solved problem 3
Video
7:44
1.5.6 Solved problem 4
Video
8:2
1.5.7 Solved problem 5
Video
10:24
1.5.8 Solved problem 6
Video
9:37
1.5.9 solved problem 7
PDF
1.5.10 Solved problem 8
PDF
1.5.11 Solved problem 9
PDF
1.6 Theory of Infrence
1.6.1 Theory of Infrence
PDF
1.6.2 Solved problem 1
Video
3:23
1.6.3 Solved problem 2
Video
6:40
1.6.4 Solved problem 3
Video
5:41
1.6.5 Solved problem 4
Video
9:00
1.6.6 Solved problem 5
PDF
1.6.7 Consistent & Inconsistent
PDF
1.6.8 Solved problem 1
Video
5:58
1.6.9 Solved problem 2
Video
10:23
1.6.10 Solved problem 3
Video
9:29
1.6.11 Solved problem 4
PDF
1.6.12 Indirect method of proof
PDF
1.6.13 Solved Problem 1
Video
7:31
1.6.14 Solved Problem 2
Video
7:59
1.6.15 Solved Problem 3
PDF
1.6.16 Solved Problem 4
PDF
1.7 The Predicate Calculus
1.7.1 The Predicate Calculus
PDF
1.7.2 Quantifiers
PDF
1.7.3 Solved problem 1
Video
2:32
1.7.4 Solved problem 2
Video
2:37
1.7.5 Solved problem 3
Video
5:1
1.7.6 Solved problem 4
Video
7:58
1.7.7 Solved problem 5
PDF
1.8 The Universe Of Discourse
1.8.1 The Universe Of Discourse
PDF
1.8.2 Solved problem 1
Video
4:54
1.8.3 Solved problem 2
Video
4:18
1.8.4 Solved problem 3
Video
4:22
1.8.5 Solved problem 4
Video
2:34
1.8.6 Solved problem 5
Video
6:25
1.9 The Theory of Inference for predicate calculus
1.9.1 The Theory of Inference for predicate calculus
PDF
1.9.2 Formulae in Quantifiers
PDF
1.9.3 Solved problem 1
Video
4:33
1.9.4 Solved problem 2
Video
6:46
1.9.5 Solved problem 3
Video
5:39
1.9.6 Solved problem 4
Video
8:35
1.9.7 Solved problem 5
Video
10:25
1.9.8 Solved problem 6
PDF
1.9.9 Solved problem 7
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1.9.10 Solved problem 8
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1.9.11 Solved problem 9
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1.9.12 Solved problem 10
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1.9.13 Solved problem 11
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1.9.14 Solved problem 12
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1.9.15 Solved problem 13
PDF
Unit - II : Combinatorics
113 Learning Materials
2.1 Mathematical Induction
2.1.1 Introduction
PDF
2.1.2 Mathematical Induction
PDF
2.1.3 Strong Induction
PDF
2.1.4 Solved Problem 1
Video
6:47
2.1.5 Solved Problem 2
Video
5:1
2.1.6 Solved Problem 3
Video
5:8
2.1.7 Solved Problem 4
Video
3:44
2.1.8 Solved Problem 5
Video
5:4
2.1.9 Solved Problem 6
Video
4:23
2.1.10 Solved Problem 7
PDF
2.1.11 Solved Problem 8
PDF
2.1.12 Solved Problem 9
PDF
2.1.13 Solved Problem 10
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2.1.14 Solved Problem 11
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2.1.15 Solved Problem 12
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2.1.16 Solved Problem 13
PDF
2.1.17 Solved Problem 14
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2.1.18 Solved Problem 15
PDF
2.1.19 Exercises
PDF
2.2 Pigeon Hole Principle
2.2.1 Introduction
PDF
2.2.2 Pigeon Hole Principle
PDF
2.2.3 The Well-ordering Property
PDF
2.2.4 Solved Problem 1
Video
2:47
2.2.5 Solved Problem 2
Video
3:48
2.2.6 Solved Problem 3
Video
3:42
2.2.7 Solved Problem 4
Video
6:48
2.2.8 Solved Problem 5
PDF
2.2.9 Solved Problem 6
PDF
2.2.10 Solved Problem 7
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2.2.11 Solved Problem 8
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2.2.12 Solved Problem 9
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2.2.13 Solved Problem 10
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2.2.14 Exercises
PDF
2.3 Permutations
2.3.1 Introduction
PDF
2.3.2 Permutations
PDF
2.3.3 Solved Problem 1
Video
4:43
2.3.4 Solved Problem 2
Video
5:11
2.3.5 Solved Problem 3
Video
5:4
2.3.6 Solved Problem 4
PDF
2.3.7 Solved Problem 5
PDF
2.3.8 Solved Problem 6
PDF
2.3.9 Solved Problem 7
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2.3.10 Solved Problem 8
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2.3.11 Solved Problem 9
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2.3.12 Solved Problem 10
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2.3.13 Solved Problem 11
PDF
2.3.14 Exercises
PDF
2.4 Combinations
2.4.1 Introduction
PDF
2.4.2 Combinations
PDF
2.4.3 Solved Problem 1
Video
4:17
2.4.4 Solved Problem 2
Video
13:30
2.4.5 Solved Problem 5
Video
5:59
2.4.6 Solved Problem 4
PDF
2.4.7 Solved Problem 5
PDF
2.4.8 Solved Problem 6
PDF
2.4.9 Solved Problem 7
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2.4.10 Solved Problem 8
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2.4.11 Solved Problem 9
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2.4.12 Solved Problem 10
PDF
2.4.13 Exercises
PDF
2.5 Recurrence Relations
2.5.1 Introduction
PDF
2.5.2 Recurrence Relations homogeneous
PDF
2.5.3 Solved Problem 1
Video
6:13
2.5.4 Solved Problem 2
Video
6:57
2.5.5 Solved Problem 3
Video
7:20
2.5.6 Solved Problem 4
Video
9:56
2.5.7 Solved Problem 5
PDF
2.5.8 Solved Problem 6
PDF
2.5.9 Solved Problem 7
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2.5.10 Solved Problem 8
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2.5.11 Solved Problem 9
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2.5.12 Solved Problem 10
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2.5.13 Solved Problem 11
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2.5.14 Recurrence Relations non-homogeneous
PDF
2.5.15 Solved Problem 1
Video
10:57
2.5.16 Solved Problem 2
Video
8:6
2.5.17 Solved Problem 3
PDF
2.5.18 Solved Problem 4
PDF
2.5.19 Solved Problem 5
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2.5.20 Solved Problem 6
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2.5.21 Solved Problem 7
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2.5.22 Solved Problem 8
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2.5.23 Solved Problem 9
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2.5.24 Exercises
PDF
2.6 Generating Functions
2.6.1 Introduction
PDF
2.6.2 Recurrence Relations – Generating Function
PDF
2.6.3 Solved Problem 1
Video
12:30
2.6.4 Solved Problem 2
Video
11:18
2.6.5 Solved Problem 3
Video
9:48
2.6.6 Solved Problem 4
Video
12:17
2.6.7 Solved Problem 5
PDF
2.6.8 Solved Problem 6
PDF
2.6.9 Solved Problem 7
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2.6.10 Solved Problem 8
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2.6.11 Solved Problem 9
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2.6.12 Solved Problem 10
PDF
2.6.13 Exercises
PDF
2.7 Inclusion and Exclusion
2.7.1 Introduction
PDF
2.7.2 The Principle of Inclusion - Exclusion
PDF
2.7.3 Solved Problem 1
Video
3:44
2.7.4 Solved Problem 2
Video
5:17
2.7.5 Solved Problem 3
Video
11:6
2.7.6 Solved Problem 4
Video
9:23
2.7.7 Solved Problem 5
Video
8:59
2.7.8 Solved Problem 6
Video
7:39
2.7.9 Solved Problem 7
PDF
2.7.10 Solved Problem 8
PDF
2.7.11 Solved Problem 9
PDF
2.7.12 Solved Problem 10
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2.7.13 Solved Problem 11
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2.7.14 Solved Problem 12
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2.7.15 Solved Problem 13
PDF
2.7.16 Exercises
PDF
Unit - III : Graphs
67 Learning Materials
3.1 Graphs
3.1.1 History of Graph Theory
PDF
3.1.2 Graph definition
PDF
3.1.3 Graph Terminology
PDF
3.1.4 Degree of a vertex
PDF
3.1.5 Types of Graphs
PDF
3.1.6 Graph Models
PDF
3.1.7 Solved problem 1
PDF
3.1.8 Solved problem 2
PDF
3.1.9 Solved problem 3
Video
3:30
3.1.10 Solved problem 4
Video
4:5
3.1.11 Solved problem 5
Video
2:44
3.1.12 Solved problem 6
PDF
3.1.13 Solved problem 7
PDF
3.1.14 Exercises
PDF
3.2 Special Graphs
3.2.1 Special types of Graphs
PDF
3.2.2 Bipartite graph
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3.2.3 Subgraph
PDF
3.2.4 Complement
PDF
3.2.5 Graph Colouring
PDF
3.2.6 Solved Problem 1
PDF
3.2.7 Solved problem 2
Video
5:52
3.2.8 Solved Problem 3
PDF
3.2.9 Solved Problem 4
PDF
3.2.10 Solved problem 5
Video
4:10
3.2.11 Solved problem 6
Video
5:19
3.2.12 Exercises
PDF
3.3 Graph Representation
3.3.1 Representation of Graphs in Computer Memory
PDF
3.3.2 Adjacency matrix
PDF
3.3.3 Incidence matrix
PDF
3.3.4 Solved problem 1
PDF
3.3.5 Solved problem 2
Video
11:48
3.3.6 Solved problem 3
PDF
3.3.7 Solved problem 4
PDF
3.3.8 Exercises
PDF
3.4 Graph Isomorphism
3.4.1 Graph Isomorphism
PDF
3.4.2 Solved problem 1
Video
9:12
3.4.3 Solved problem 2
Video
7:49
3.4.4 Solved problem 3
PDF
3.4.5 Solved problem 4
Video
5:23
3.4.6 Solved problem 5
Video
6:44
3.4.7 Solved problem 6
Video
7:48
3.4.8 Solved problem 7
Video
4:52
3.4.9 Solved problem 8
Video
7:12
3.4.10 Exercises
PDF
3.5 Connectivity
3.5.1 Paths, Circuits and Connectedness
PDF
3.5.2 Paths and Circuits
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3.5.3 Paths in Acquaintanceship Graphs
PDF
3.5.4 Connectedness
PDF
3.5.5 Connected component
PDF
3.5.6 Solved problem 1
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3.5.7 Solved problem 2
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3.5.8 Solved problem 3
PDF
3.5.9 Solved problem 4
PDF
3.5.10 Solved problem 5
PDF
3.5.11 Solved problem 6
Video
11:48
3.5.12 Solved problem 7
Video
2:39
3.5.13 Solved problem 8
Video
3:41
3.5.14 Solved problem 9
PDF
3.6 Euler and Hamilton Paths
3.6.1 Euler Path and Circuits
PDF
3.6.2 Hamilton path and circuits
PDF
3.6.3 Dirac’s Theorem
PDF
3.6.4 Solved problem 1
Video
6:31
3.6.5 Solved problem 2
Video
5:54
3.6.6 Solved problem 3
Video
4:22
3.6.7 Solved problem 4
PDF
3.6.8 Solved problem 5
PDF
3.6.9 Exercises
PDF
Unit - IV : Algebraic structures
60 Learning Materials
4.1 Algebraic systems
4.1.1 Introduction of Algebraic structures
PDF
4.1.2 BINARY and N – ARY operations
PDF
4.1.3 Algebraic System
PDF
4.2 Semigroups and monoids
4.2.1 Semigroup
PDF
4.2.2 Monoid
PDF
4.2.3 Cyclic monoids (Cyclic semigroups)
PDF
4.2.4 Morphism of Semigroups
PDF
4.2.5 Morphism of Monoids
PDF
4.2.6 Solved Problem 1
Video
4:59
4.2.7 Solved Problem 2
Video
4:59
4.2.8 Solved Problem 3
Video
9:30
4.3 Groups
4.3.1 Group
PDF
4.3.2 Definitions
PDF
4.3.3 Properties of Group
PDF
4.3.4 Solved problem 1
Video
4:56
4.3.5 Solved problem 2
Video
11:7
4.3.6 Solved problem 3
Video
6:36
4.3.7 solved problem 4
PDF
4.3.8 solved problem 5
PDF
4.3.9 solved problem 6
PDF
4.3.10 Solved problem 7
Video
8:41
4.3.11 Solved problem 8
Video
7:23
4.3.12 Permutation Groups and Dihedral Group
PDF
4.3.13 Solved Problem 1
Video
12:26
4.3.14 Solved Problem 2
Video
6:15
4.4 Subgroups
4.4.1 Subgroup
PDF
4.4.2 Necessary and sufficient condition for a subgroup
PDF
4.4.3 Theorem 1
PDF
4.4.4 Theorem 2
Video
2:45
4.4.5 Group Homomorphism
PDF
4.4.6 Theorem 1
PDF
4.4.7 Theorem 2
PDF
4.4.8 Theorem 3
PDF
4.4.9 Cayley’s theorem
Video
13:48
4.4.10 Solved problem 1
Video
7:14
4.5 Homomorphism and Isomorphism
4.5.1 Kernel of a Homomorphism
PDF
4.5.2 Theorem 1
Video
4:11
4.5.3 Theorem 2
PDF
4.5.4 Isomorphism
PDF
4.5.5 Fundamental thereom on homomorphism of groups
Video
13:28
4.5.6 Theorem 2
Video
3:46
4.5.7 Solved problem 1
Video
7:3
4.5.8 Solved problem 2
Video
6:2
4.5.9 Solved problem 3
Video
3:12
4.5.10 solved problem 4
PDF
4.6 Cosets and lagrange’s theorem
4.6.1 Cosets and lagrange’s theorem
PDF
4.6.2 Lagrange's theorem
Video
1:39
4.6.3 Normal Subgroup
PDF
4.6.4 Natural Homomorphism
PDF
4.6.5 Theorem 1
Video
3:5
4.6.6 Theorem 2
Video
2:50
4.6.7 Theorem 3
Video
2:43
4.6.8 Theorem 4
Video
1:49
4.6.9 Cyclic Group
PDF
4.7 Definitions and examples of rings and fields
4.7.1 Definitions and examples of rings and fields
PDF
4.7.2 Theorem 1
PDF
4.7.3 Theorem 2
Video
4:22
4.7.4 solved problem 1
Video
3:36
4.7.5 solved problem 2
PDF
4.7.6 solved problem 3
Video
13:36
Unit - V : Lattices and boolean algebra
76 Learning Materials
5.1 Partially Ordered Set (Poset)
5.1.1 Introduction
PDF
5.1.2 Product of Sets
PDF
5.1.3 Relation
PDF
5.1.4 Partial Order Relation
PDF
5.1.5 Partially Ordered Set or Poset
PDF
5.1.6 Comparable Property
PDF
5.1.7 Hasse Diagram
PDF
5.1.8 Solved Problem 1
PDF
5.1.9 Solved Problem 2
PDF
5.1.10 Solved Problem 3
Video
6:37
5.1.11 Solved Problem 4
PDF
5.1.12 Solved Problem 5
Video
7:13
5.1.13 Solved Problem 6
PDF
5.1.14 Upper and Lower Bound
PDF
5.1.15 Solved Problem 1
Video
10:16
5.1.16 Solved Problem 2
PDF
5.1.17 Solved Problem 3
Video
11:27
5.1.18 Solved problem 4
Video
7:00
5.1.19 Solved Problem 5
PDF
5.1.20 Solved problem 6
PDF
5.1.20 Solved Problem 6
Video
6:32
5.1.21 Solved Problem 7
PDF
5.1.22 Exercises
PDF
5.2 Lattice
5.2.1 Introduction
PDF
5.2.2 Lattice
PDF
5.2.3 Solved Problem 1
Video
6:22
5.2.4 Solved Problem 2
PDF
5.2.5 Solved Problem 3
PDF
5.2.6 Solved Problem 4
PDF
5.2.7 Properties of lattice
Video
14:00
5.2.8 Theorem 1
Video
6:6
5.2.9 Theorem 2
PDF
5.2.10 Theorem 3 (Isotonicity)
Video
8:46
5.2.11 Theorem 4 (distributive Inequality)
Video
12:23
5.2.12 Exercises
PDF
5.3 Types of Lattice
5.3.1 Duality in Lattice
PDF
5.3.2 Theorem 1 (Any chain)
Video
9:4
5.3.3 Theorem 2 (Modular Inequality)
Video
5:28
5.3.4 Modular Lattice
PDF
5.3.5 Solved Problem 1
PDF
5.3.6 Solved Problem 2
Video
7:47
5.3.7 Theorem 1
PDF
5.3.8 Solved Problem 1
Video
3:44
5.3.9 Solved Problem 2
Video
6:4
5.3.10 Lattice as a Algebraic system
PDF
5.3.11 Lattice Homomorphism
PDF
5.3.12 Theorem 1
PDF
5.3.13 Direct Product of Lattice
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5.3.14 Theorem 2
PDF
5.3.15 Some Special Lattices
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5.3.16 Complemented Lattice
PDF
5.3.17 Solved Problem 1
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5.3.18 Solved Problem 2
PDF
5.3.19 Solved Problem 3
PDF
5.3.20 Exercises
PDF
5.4 Boolean Algebra
5.4.1 Introduction
PDF
5.4.2 Boolean Algebra
PDF
5.4.3 Theorem 1 (Idempotent laws)
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5.4.4 Theorem 2 and 3
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5.4.5 Theorem 4
PDF
5.4.6 Theorem 5
PDF
5.4.7 Theorem 6
PDF
5.4.8 Theorem 7 (De-Morgan’s law)
Video
11:52
5.4.9 Theorem 8
Video
6:5
5.4.10 Solved Problem 1
PDF
5.4.11 Solved Problem 2
PDF
5.4.12 Solved Problem 3
PDF
5.4.13 Solved Problem 4
Video
7:54
5.4.14 Solved Problem 5
Video
6:51
5.4.15 Solved Problem 6
Video
9:28
5.4.16 Dual
PDF
5.4.17 Duality principle
PDF
5.4.18 Sub-algebra and Homomorphisms
PDF
5.4.19 Solved Problem 1
PDF
5.4.20 Boolean homomorphism
PDF
5.4.21 Exercises
PDF
Important Q&A
83 Learning Materials
1. Logic and Proofs
1.1 Part A: Q&A
PDF
1.2 Part B: Q&A - 1
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1.3 Part B: Q&A - 2
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1.4 Part B: Q&A - 3
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1.5 Part B: Q&A - 4
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1.6 Part B: Q&A - 5
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1.7 Part B: Q&A - 6
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1.8 Part B: Q&A - 7
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1.9 Part B: Q&A - 8
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1.10 Part B: Q&A - 9
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1.11 Part B: Q&A - 10
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1.12 Part B: Q&A - 11
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1.13 Part B: Q&A - 12
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2. Combinatorics
2.1 Part A: Q&A
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2.2 Part B: Q&A - 1
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2.3 Part B: Q&A - 2
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2.4 Part B: Q&A - 3
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2.5 Part B: Q&A - 4
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2.6 Part B: Q&A - 5
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2.7 Part B: Q&A - 6
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2.8 Part B: Q&A - 7
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2.9 Part B: Q&A - 8
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2.10 Part B: Q&A - 9
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2.11 Part B: Q&A - 10
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2.12 Part B: Q&A - 11
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2.13 Part B: Q&A - 12
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2.14 Part B: Q&A - 13
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2.15 Part B: Q&A - 14
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2.16 Part B: Q&A - 15
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2.17 Part B: Q&A - 16
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2.18 Part B: Q&A - 17
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2.19 Part B: Q&A - 18
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2.20 Part B: Q&A - 19
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2.21 Part B: Q&A - 20
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2.22 Part B: Q&A - 21
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3. Graphs
3.1 Part A: Q&A
PDF
3.2 Part B: Q&A - 1
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3.3 Part B: Q&A - 2
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3.4 Part B: Q&A - 3
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3.5 Part B: Q&A - 4
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3.6 Part B: Q&A - 5
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3.7 Part B: Q&A - 6
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3.8 Part B: Q&A - 7
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3.9 Part B: Q&A - 8
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3.10 Part B: Q&A - 9
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3.11 Part B: Q&A - 10
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3.12 Part B: Q&A - 11
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4. Algebraic structures
4.1 Part A: Q&A
PDF
4.2 Part B: Q&A - 1
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4.3 Part B: Q&A - 2
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4.4 Part B: Q&A - 3
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4.5 Part B: Q&A - 4
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4.6 Part B: Q&A - 5
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4.7 Part B: Q&A - 6
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4.8 Part B: Q&A - 7
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4.9 Part B: Q&A - 8
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4.10 Part B: Q&A - 9
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4.11 Part B: Q&A - 10
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4.12 Part B: Q&A - 11
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4.13 Part B: Q&A - 12
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4.14 Part B: Q&A - 13
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4.15 Part B: Q&A - 14
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4.16 Part B: Q&A - 15
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4.17 Part B: Q&A - 16
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5. Lattices and Boolean Algebra
5.1 Part A: (Q&A)
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5.2 Part B: Q&A - 1
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5.3 Part B: Q&A - 2
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5.4 Part B: Q&A - 3
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5.5 Part B: Q&A - 4
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5.6 Part B: Q&A - 5
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5.7 Part B: Q&A - 6
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5.8 Part B: Q&A - 7
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5.9 Part B: Q&A - 8
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5.10 Part B: Q&A - 9
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5.11 Part B: Q&A - 10
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5.12 Part B: Q&A - 11
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5.13 Part B: Q&A - 12
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5.14 Part B: Q&A - 13
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5.15 Part B: Q&A - 14
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5.16 Part B: Q&A - 15
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5.17 Part B: Q&A - 16
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5.18 Part B: Q&A - 17
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5.19 Part B: Q&A - 18
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Course Instructor
Promath
787 Courses • 165783 Students
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