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
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1.1.3 Proposition and connectives
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1.1.4 Five basic connectives
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1.1.5 Statement formula
PDF
1.1.6 Solved problem 1
Video
00:02:31
1.1.7 Solved problem 2
Video
00:04:12
1.1.8 Solved problem 3
Video
00:03:08
1.1.9 Solved problem 4
Video
00:03:07
1.1.10 Solved problem 5
Video
00:03:41
1.1.11 Solved problem 6
Video
00:04:53
1.1.12 Solved problem 7
Video
00:05:00
1.1.13 Solved problem 8
Video
00:04:33
1.2 Tautology
1.2.1 Tautology
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1.2.2 Solved problem 1
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00:04:12
1.2.3 Solved problem 2
Video
00:05:30
1.2.4 Solved problem 3
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1.2.5 Solved problem 4
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1.2.6 Solved problem 5
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1.2.7 Equivalence of formulas
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1.2.8 Solved problem 1
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00:04:12
1.2.9 Solved problem 2
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00:06:37
1.2.10 Solved problem 3
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00:04:02
1.2.11 Solved problem 4
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1.2.12 Solved problem 5
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1.2.13 Tautology Implications
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1.2.14 Solved problem 1
Video
00:03:39
1.3 Converse, Contrapositive And Inverse Propositions
1.3.1 Converse, Contrapositive And Inverse Propositions
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1.3.2 Solved problem 1
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00:02:43
1.3.3 Solved problem 2
Video
00:02:30
1.3.4 Solved problem 3
Video
00:02:41
1.3.5 Solved problem 4
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00:06:26
1.3.6 Functionally complete set
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1.3.7 Examples
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1.4 Normal Form
1.4.1 Normal Form
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1.4.2 Implication Rules
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1.4.3 Disjunctive normal form (DNF)& Conjunctive normal form(CNF)
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1.4.4 Solved problem 1&2
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1.4.5 Solved problem 3
Video
00:06:30
1.4.6 Solved problem 4
Video
00:08:21
1.4.7 Solved problem 5
Video
00:06:05
1.4.8 Solved problem 6
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1.5 principal normal forms
1.5.1 Minterms & Maxterms
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1.5.2 PDNF & PCNF
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1.5.3 Solved problem 1
Video
00:06:34
1.5.4 Solved problem 2
Video
00:05:23
1.5.5 Solved problem 3
Video
00:07:44
1.5.6 Solved problem 4
Video
00:08:02
1.5.7 Solved problem 5
Video
00:10:24
1.5.8 Solved problem 6
Video
00:09:37
1.5.9 solved problem 7
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1.5.10 Solved problem 8
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1.5.11 Solved problem 9
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1.6 Theory of Infrence
1.6.1 Theory of Infrence
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1.6.2 Solved problem 1
Video
00:03:23
1.6.3 Solved problem 2
Video
00:06:40
1.6.4 Solved problem 3
Video
00:05:41
1.6.5 Solved problem 4
Video
00:09:00
1.6.6 Solved problem 5
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1.6.7 Consistent & Inconsistent
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1.6.8 Solved problem 1
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00:05:58
1.6.9 Solved problem 2
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00:10:23
1.6.10 Solved problem 3
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00:09:29
1.6.11 Solved problem 4
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1.6.12 Indirect method of proof
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1.6.13 Solved Problem 1
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00:07:31
1.6.14 Solved Problem 2
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00:07:59
1.6.15 Solved Problem 3
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1.6.16 Solved Problem 4
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1.7 The Predicate Calculus
1.7.1 The Predicate Calculus
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1.7.2 Quantifiers
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1.7.3 Solved problem 1
Video
00:02:32
1.7.4 Solved problem 2
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00:02:37
1.7.5 Solved problem 3
Video
00:05:01
1.7.6 Solved problem 4
Video
00:07:58
1.7.7 Solved problem 5
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1.8 The Universe Of Discourse
1.8.1 The Universe Of Discourse
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1.8.2 Solved problem 1
Video
00:04:54
1.8.3 Solved problem 2
Video
00:04:18
1.8.4 Solved problem 3
Video
00:04:22
1.8.5 Solved problem 4
Video
00:02:34
1.8.6 Solved problem 5
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00:06:25
1.9 The Theory of Inference for predicate calculus
1.9.1 The Theory of Inference for predicate calculus
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1.9.2 Formulae in Quantifiers
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1.9.3 Solved problem 1
Video
00:04:33
1.9.4 Solved problem 2
Video
00:06:46
1.9.5 Solved problem 3
Video
00:05:39
1.9.6 Solved problem 4
Video
00:08:35
1.9.7 Solved problem 5
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00:10:25
1.9.8 Solved problem 6
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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
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Unit - II : Combinatorics
113 Learning Materials
2.1 Mathematical Induction
2.1.1 Introduction
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2.1.2 Mathematical Induction
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2.1.3 Strong Induction
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2.1.4 Solved Problem 1
Video
00:06:47
2.1.5 Solved Problem 2
Video
00:05:01
2.1.6 Solved Problem 3
Video
00:05:08
2.1.7 Solved Problem 4
Video
00:03:44
2.1.8 Solved Problem 5
Video
00:05:04
2.1.9 Solved Problem 6
Video
00:04:23
2.1.10 Solved Problem 7
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2.1.11 Solved Problem 8
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2.1.12 Solved Problem 9
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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
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2.1.17 Solved Problem 14
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2.1.18 Solved Problem 15
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2.1.19 Exercises
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2.2 Pigeon Hole Principle
2.2.1 Introduction
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2.2.2 Pigeon Hole Principle
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2.2.3 The Well-ordering Property
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2.2.4 Solved Problem 1
Video
00:02:47
2.2.5 Solved Problem 2
Video
00:03:48
2.2.6 Solved Problem 3
Video
00:03:42
2.2.7 Solved Problem 4
Video
00:06:48
2.2.8 Solved Problem 5
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2.2.9 Solved Problem 6
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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
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2.3 Permutations
2.3.1 Introduction
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2.3.2 Permutations
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2.3.3 Solved Problem 1
Video
00:04:43
2.3.4 Solved Problem 2
Video
00:05:11
2.3.5 Solved Problem 3
Video
00:05:04
2.3.6 Solved Problem 4
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2.3.7 Solved Problem 5
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2.3.8 Solved Problem 6
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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
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2.3.14 Exercises
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2.4 Combinations
2.4.1 Introduction
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2.4.2 Combinations
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2.4.3 Solved Problem 1
Video
00:04:17
2.4.4 Solved Problem 2
Video
00:13:30
2.4.5 Solved Problem 5
Video
00:05:59
2.4.6 Solved Problem 4
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2.4.7 Solved Problem 5
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2.4.8 Solved Problem 6
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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
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2.4.13 Exercises
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2.5 Recurrence Relations
2.5.1 Introduction
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2.5.2 Recurrence Relations homogeneous
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2.5.3 Solved Problem 1
Video
00:06:13
2.5.4 Solved Problem 2
Video
00:06:57
2.5.5 Solved Problem 3
Video
00:07:20
2.5.6 Solved Problem 4
Video
00:09:56
2.5.7 Solved Problem 5
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2.5.8 Solved Problem 6
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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
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2.5.15 Solved Problem 1
Video
00:10:57
2.5.16 Solved Problem 2
Video
00:08:06
2.5.17 Solved Problem 3
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2.5.18 Solved Problem 4
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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
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2.6 Generating Functions
2.6.1 Introduction
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2.6.2 Recurrence Relations – Generating Function
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2.6.3 Solved Problem 1
Video
00:12:30
2.6.4 Solved Problem 2
Video
00:11:18
2.6.5 Solved Problem 3
Video
00:09:48
2.6.6 Solved Problem 4
Video
00:12:17
2.6.7 Solved Problem 5
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2.6.8 Solved Problem 6
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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
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2.6.13 Exercises
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2.7 Inclusion and Exclusion
2.7.1 Introduction
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2.7.2 The Principle of Inclusion - Exclusion
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2.7.3 Solved Problem 1
Video
00:03:44
2.7.4 Solved Problem 2
Video
00:05:17
2.7.5 Solved Problem 3
Video
00:11:06
2.7.6 Solved Problem 4
Video
00:09:23
2.7.7 Solved Problem 5
Video
00:08:59
2.7.8 Solved Problem 6
Video
00:07:39
2.7.9 Solved Problem 7
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2.7.10 Solved Problem 8
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2.7.11 Solved Problem 9
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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
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2.7.16 Exercises
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Unit - III : Graphs
67 Learning Materials
3.1 Graphs
3.1.1 History of Graph Theory
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3.1.2 Graph definition
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3.1.3 Graph Terminology
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3.1.4 Degree of a vertex
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3.1.5 Types of Graphs
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3.1.6 Graph Models
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3.1.7 Solved problem 1
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3.1.8 Solved problem 2
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3.1.9 Solved problem 3
Video
00:03:30
3.1.10 Solved problem 4
Video
00:04:05
3.1.11 Solved problem 5
Video
00:02:44
3.1.12 Solved problem 6
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3.1.13 Solved problem 7
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3.1.14 Exercises
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3.2 Special Graphs
3.2.1 Special types of Graphs
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3.2.2 Bipartite graph
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3.2.3 Subgraph
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3.2.4 Complement
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3.2.5 Graph Colouring
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3.2.6 Solved Problem 1
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3.2.7 Solved problem 2
Video
00:05:52
3.2.8 Solved Problem 3
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3.2.9 Solved Problem 4
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3.2.10 Solved problem 5
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00:04:10
3.2.11 Solved problem 6
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00:05:19
3.2.12 Exercises
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3.3 Graph Representation
3.3.1 Representation of Graphs in Computer Memory
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3.3.2 Adjacency matrix
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3.3.3 Incidence matrix
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3.3.4 Solved problem 1
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3.3.5 Solved problem 2
Video
00:11:48
3.3.6 Solved problem 3
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3.3.7 Solved problem 4
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3.3.8 Exercises
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3.4 Graph Isomorphism
3.4.1 Graph Isomorphism
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3.4.2 Solved problem 1
Video
00:09:12
3.4.3 Solved problem 2
Video
00:07:49
3.4.4 Solved problem 3
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3.4.5 Solved problem 4
Video
00:05:23
3.4.6 Solved problem 5
Video
00:06:44
3.4.7 Solved problem 6
Video
00:07:48
3.4.8 Solved problem 7
Video
00:04:52
3.4.9 Solved problem 8
Video
00:07:12
3.4.10 Exercises
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3.5 Connectivity
3.5.1 Paths, Circuits and Connectedness
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3.5.2 Paths and Circuits
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3.5.3 Paths in Acquaintanceship Graphs
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3.5.4 Connectedness
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3.5.5 Connected component
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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
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3.5.9 Solved problem 4
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3.5.10 Solved problem 5
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3.5.11 Solved problem 6
Video
00:11:48
3.5.12 Solved problem 7
Video
00:02:39
3.5.13 Solved problem 8
Video
00:03:41
3.5.14 Solved problem 9
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3.6 Euler and Hamilton Paths
3.6.1 Euler Path and Circuits
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3.6.2 Hamilton path and circuits
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3.6.3 Dirac’s Theorem
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3.6.4 Solved problem 1
Video
00:06:31
3.6.5 Solved problem 2
Video
00:05:54
3.6.6 Solved problem 3
Video
00:04:22
3.6.7 Solved problem 4
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3.6.8 Solved problem 5
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3.6.9 Exercises
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Unit - IV : Algebraic structures
60 Learning Materials
4.1 Algebraic systems
4.1.1 Introduction of Algebraic structures
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4.1.2 BINARY and N – ARY operations
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4.1.3 Algebraic System
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4.2 Semigroups and monoids
4.2.1 Semigroup
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4.2.2 Monoid
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4.2.3 Cyclic monoids (Cyclic semigroups)
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4.2.4 Morphism of Semigroups
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4.2.5 Morphism of Monoids
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4.2.6 Solved Problem 1
Video
00:04:59
4.2.7 Solved Problem 2
Video
00:04:59
4.2.8 Solved Problem 3
Video
00:09:30
4.3 Groups
4.3.1 Group
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4.3.2 Definitions
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4.3.3 Properties of Group
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4.3.4 Solved problem 1
Video
00:04:56
4.3.5 Solved problem 2
Video
00:11:07
4.3.6 Solved problem 3
Video
00:06:36
4.3.7 solved problem 4
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4.3.8 solved problem 5
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4.3.9 solved problem 6
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4.3.10 Solved problem 7
Video
00:08:41
4.3.11 Solved problem 8
Video
00:07:23
4.3.12 Permutation Groups and Dihedral Group
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4.3.13 Solved Problem 1
Video
00:12:26
4.3.14 Solved Problem 2
Video
00:06:15
4.4 Subgroups
4.4.1 Subgroup
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4.4.2 Necessary and sufficient condition for a subgroup
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4.4.3 Theorem 1
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4.4.4 Theorem 2
Video
00:02:45
4.4.5 Group Homomorphism
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4.4.6 Theorem 1
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4.4.7 Theorem 2
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4.4.8 Theorem 3
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4.4.9 Cayley’s theorem
Video
00:13:48
4.4.10 Solved problem 1
Video
00:07:14
4.5 Homomorphism and Isomorphism
4.5.1 Kernel of a Homomorphism
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4.5.2 Theorem 1
Video
00:04:11
4.5.3 Theorem 2
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4.5.4 Isomorphism
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4.5.5 Fundamental thereom on homomorphism of groups
Video
00:13:28
4.5.6 Theorem 2
Video
00:03:46
4.5.7 Solved problem 1
Video
00:07:03
4.5.8 Solved problem 2
Video
00:06:02
4.5.9 Solved problem 3
Video
00:03:12
4.5.10 solved problem 4
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4.6 Cosets and lagrange’s theorem
4.6.1 Cosets and lagrange’s theorem
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4.6.2 Lagrange's theorem
Video
00:05:11
4.6.3 Normal Subgroup
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4.6.4 Natural Homomorphism
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4.6.5 Theorem 1
Video
00:03:05
4.6.6 Theorem 2
Video
00:02:50
4.6.7 Theorem 3
Video
00:02:43
4.6.8 Theorem 4
Video
00:01:49
4.6.9 Cyclic Group
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4.7 Definitions and examples of rings and fields
4.7.1 Definitions and examples of rings and fields
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4.7.2 Theorem 1
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4.7.3 Theorem 2
Video
00:04:22
4.7.4 solved problem 1
Video
00:03:36
4.7.5 solved problem 2
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4.7.6 solved problem 3
Video
00:13:36
Unit - V : Lattices and boolean algebra
76 Learning Materials
5.1 Partially Ordered Set (Poset)
5.1.1 Introduction
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5.1.2 Product of Sets
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5.1.3 Relation
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5.1.4 Partial Order Relation
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5.1.5 Partially Ordered Set or Poset
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5.1.6 Comparable Property
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5.1.7 Hasse Diagram
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5.1.8 Solved Problem 1
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5.1.9 Solved Problem 2
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5.1.10 Solved Problem 3
Video
00:06:37
5.1.11 Solved Problem 4
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5.1.12 Solved Problem 5
Video
00:07:13
5.1.13 Solved Problem 6
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5.1.14 Upper and Lower Bound
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5.1.15 Solved Problem 1
Video
00:10:16
5.1.16 Solved Problem 2
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5.1.17 Solved Problem 3
Video
00:11:27
5.1.18 Solved problem 4
Video
00:07:00
5.1.19 Solved Problem 5
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5.1.20 Solved problem 6
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5.1.20 Solved Problem 6
Video
00:06:32
5.1.21 Solved Problem 7
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5.1.22 Exercises
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5.2 Lattice
5.2.1 Introduction
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5.2.2 Lattice
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5.2.3 Solved Problem 1
Video
00:06:22
5.2.4 Solved Problem 2
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5.2.5 Solved Problem 3
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5.2.6 Solved Problem 4
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5.2.7 Properties of lattice
Video
00:14:00
5.2.8 Theorem 1
Video
00:06:06
5.2.9 Theorem 2
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5.2.10 Theorem 3 (Isotonicity)
Video
00:08:46
5.2.11 Theorem 4 (distributive Inequality)
Video
00:12:23
5.2.12 Exercises
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5.3 Types of Lattice
5.3.1 Duality in Lattice
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5.3.2 Theorem 1 (Any chain)
Video
00:09:04
5.3.3 Theorem 2 (Modular Inequality)
Video
00:05:28
5.3.4 Modular Lattice
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5.3.5 Solved Problem 1
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5.3.6 Solved Problem 2
Video
00:07:47
5.3.7 Theorem 1
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5.3.8 Solved Problem 1
Video
00:03:44
5.3.9 Solved Problem 2
Video
00:06:04
5.3.10 Lattice as a Algebraic system
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5.3.11 Lattice Homomorphism
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5.3.12 Theorem 1
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5.3.13 Direct Product of Lattice
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5.3.14 Theorem 2
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5.3.15 Some Special Lattices
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5.3.16 Complemented Lattice
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5.3.17 Solved Problem 1
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5.3.18 Solved Problem 2
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5.3.19 Solved Problem 3
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5.3.20 Exercises
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5.4 Boolean Algebra
5.4.1 Introduction
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5.4.2 Boolean Algebra
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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
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5.4.6 Theorem 5
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5.4.7 Theorem 6
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5.4.8 Theorem 7 (De-Morgan’s law)
Video
00:11:52
5.4.9 Theorem 8
Video
00:06:05
5.4.10 Solved Problem 1
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5.4.11 Solved Problem 2
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5.4.12 Solved Problem 3
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5.4.13 Solved Problem 4
Video
00:07:54
5.4.14 Solved Problem 5
Video
00:06:51
5.4.15 Solved Problem 6
Video
00:09:28
5.4.16 Dual
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5.4.17 Duality principle
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5.4.18 Sub-algebra and Homomorphisms
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5.4.19 Solved Problem 1
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5.4.20 Boolean homomorphism
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5.4.21 Exercises
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Important Q&A
83 Learning Materials
1. Logic and Proofs
1.1 Part A: Q&A
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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
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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
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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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