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Inclusion vs. Membership (Solved Problem)
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Classroom Contents
Discrete Mathematics
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- 1 Introduction to Discrete Mathematics
- 2 Motivation & Introduction to Propositional Logic
- 3 Propositional Logic, Propositional Variables & Compound Propositions
- 4 Logical Operators − Negation, Conjunction & Disjunction
- 5 Logical Operators − Exclusive OR
- 6 Logical Operators − Implication (Part 1)
- 7 Logical Operators − Implication (Part 2)
- 8 Logical Operators − Implication (Part 3)
- 9 Converse, Contrapositive and Inverse
- 10 Logical Operators − Biconditional Operator
- 11 Propositional Logic − Precedence of Logical Operators
- 12 Translating Sentences into Logical Expressions
- 13 Propositional Logic − Puzzle 1
- 14 Propositional Logic − Puzzle 2
- 15 Propositional Logic (Solved Problem 1)
- 16 Tautology, Contradiction, Contingency & Satisfiability
- 17 Propositional Logic − Logical Equivalences
- 18 Propositional Logic (Solved Problem 2)
- 19 Propositional Logic (Solved Problem 3)
- 20 Propositional Logic (Solved Problem 4)
- 21 Propositional Logic (Solved Problem 5)
- 22 Propositional Logic (Solved Problem 6)
- 23 Propositional Logic (Solved Problem 7)
- 24 Rules of Inference - Basic Terminology
- 25 Rules of Inference - Definition & Types of Inference Rules
- 26 Arguments Building Using Rules of Inference (Part 1)
- 27 Arguments Building Using Rules of Inference (Part 2)
- 28 Checking The Validity of An Argument (Shortcut Method)
- 29 Rules of Inference in Propositional Logic (Solved Problem 1)
- 30 Rules of Inference in Propositional Logic (Solved Problem 2)
- 31 The Limitation of Propositional Logic
- 32 Introduction to First Order Logic
- 33 Finding The Truth Values of Predicates (Examples)
- 34 Quantifiers
- 35 Universal Quantifiers
- 36 Universal Quantifiers - Counter Examples
- 37 Expressing Quantifications in English
- 38 Existential Quantifiers
- 39 Existential Quantifiers - Examples
- 40 Quantifiers with Restricted Domain
- 41 Logical Equivalences Involving Predicates & Quantifiers (Part 1)
- 42 Logical Equivalences Involving Predicates & Quantifiers (Part 2)
- 43 Negating the Quantified Expressions (Part 1)
- 44 Negating the Quantified Expressions (Part 2)
- 45 Negating the Quantified Expressions (Examples)
- 46 Translating English Sentences to Logical Expressions
- 47 First Order Logic (Solved Problems) - Part 1
- 48 First Order Logic (Solved Problems) - Part 2
- 49 First Order Logic (Solved Problems) - Part 3
- 50 First Order Logic (Solved Problems) - Part 4
- 51 First Order Logic (Solved Problems) - Part 5
- 52 Introduction to Nested Quantifiers
- 53 Nested Quantifiers (Solved Example 1)
- 54 Nested Quantifiers (Solved Example 2)
- 55 Nested Quantifiers (Solved Example 3)
- 56 Nested Quantifiers (Translating English Statements) - Example 1
- 57 Nested Quantifiers (Translating English Statements) - Example 2
- 58 Nested Quantifiers (Translating English Statements) - Example 3
- 59 Nested Quantifiers (Translating English Statements) - Example 4
- 60 Nested Quantifiers (Translating English Statements) - Example 5
- 61 Negating the Nested Quantifiers
- 62 Negating the Nested Quantifiers (Example 2)
- 63 Negating the Nested Quantifiers (Example 3)
- 64 The Resolution Principle (Preliminaries)
- 65 The Resolution Principle (Proof of Theorem)
- 66 The Resolution Principle (Proving if an Argument is Valid)
- 67 The Resolution Principle (Solved Problems)
- 68 Fallacies
- 69 Rules of Inference for Quantified Statements (Part 1)
- 70 Rules of Inference for Quantified Statements (Part 2)
- 71 Universal Modus Ponens Rule
- 72 Universal Modus Tollens Rule
- 73 Set Theory (Basics of Sets)
- 74 Set Representation
- 75 Inclusion and Equality
- 76 Inclusion vs. Membership
- 77 Inclusion vs. Membership (Solved Problem)
- 78 Types of Sets - Universal, Null, and Singleton
- 79 Null Set (Solved Problem)
- 80 Non-Empty Set (Important Theorem)
- 81 Power Set
- 82 Power Set (Solved Problems)
- 83 Power Set (GATE Problem 1)
- 84 Power Set (GATE Problem 2)
- 85 Cardinality of Sets
- 86 Cartesian Product
- 87 Cartesian Product (Solved Problems)
- 88 Set Operations (Intersection & Union with Venn Diagram)
- 89 Set Difference and Set Complement
- 90 Set Operations (Solved Problems)
- 91 Set Identities (Part 1)
- 92 Set Identities (Part 2)
- 93 Set Identities (Part 3)
- 94 Set Operations (Solved Problem 1)
- 95 Set Operations (Solved Problem 2)
- 96 Symmetric Difference
- 97 Set Operations (GATE Problems)
- 98 Set Operations (GATE and TIFR Problem)
- 99 Introduction to Relations
- 100 Types of Relations (Part 1)
- 101 Types of Relations (Part 2)
- 102 Types of Relations (Solved Problem)
- 103 Types of Relations (GATE Problems) - Set 1
- 104 Types of Relations (GATE Problems) - Set 2
- 105 Operations on Relations
- 106 Composition of Relations
- 107 Composition of Relation with Itself
- 108 Representation of Relations
- 109 Closure of Relations – Part 1
- 110 Closure of Relations – Part 2
- 111 Closure of Relations (Solved Problems) - Set 1
- 112 Warshall's Algorithm (Finding the Transitive Closure)
- 113 Closure of Relations (Solved Problems) - Set 2
- 114 Closure of Relations - GATE Problem
- 115 Equivalence Relation
- 116 Equivalence Relation (Solved Problems)
- 117 Equivalence Relation (GATE Problems) - Set 1
- 118 Equivalence Relation (GATE Problems) - Set 2
- 119 Equivalence Relation (GATE Problem)
- 120 Equivalence Classes
- 121 Congruence Modulo m
- 122 Modulus of Negative Numbers
- 123 Equivalence Classes and Partitions
- 124 Equivalence Classes and Partitions (Solved Problems)
- 125 Introduction to Partial Ordering
- 126 Partial Orderings (Solved Problems) - Set 1
- 127 Partial Orderings (Solved Problems) - Set 2
- 128 Hasse Diagram
- 129 Hasse Diagram (Solved Problems) - Set 1
- 130 Hasse Diagram (Solved Problems) - Set 2
- 131 Poset (Minimal and Maximal Elements)
- 132 Poset (Least and Greatest Elements)
- 133 Poset (Lower and Upper Bounds)
- 134 Poset (Least Upper Bound and Greatest Lower Bound)
- 135 Hasse Diagram (Solved Problems) - Set 3
- 136 Symbols for Partial Order
- 137 Meet Semilattice
- 138 Join Semilattice
- 139 Lattice
- 140 Lattice (GATE Problems) - Set 1
- 141 Complete and Bounded Lattice
- 142 Lattice (Complement of an Element)
- 143 Lattice (GATE Problems) - Set 2
- 144 Complemented Lattice
- 145 Distributive Lattice
- 146 Functions | Chapter-7 | Discrete Mathematics | nesoacademy.org
- 147 Counting | Chapter-8 | Discrete Mathematics | nesoacademy.org
- 148 Permutations & Combinations | Chapter-9 | Discrete Mathematics | nesoacademy.org
