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Computer Science

31Propositions and Truth Values
32Logical Negation
33Logical Conjunction (AND)
34Logical Disjunction (OR)
35Exclusive OR (XOR)
36Conditional Statements (Implication)
37Converse, Inverse, and Contrapositive
38Biconditional Statements
39Compound Propositions and Precedence
40Logical Equivalence
41De Morgan's Laws
42Distributive and Associative Laws
43Tautologies and Contradictions
44Logical Inference Rules
45Normal Forms: CNF and DNF
46Predicates and Propositional Functions
47Universal Quantifier (∀)
48Existential Quantifier (∃)
49Negating Quantified Statements
50Nested Quantifiers
51Translating English to Predicate Logic
52Translating Predicate Logic to English
53Quantifier Scope and Binding
54Uniqueness Quantifier (∃!)
55Quantifiers Over Restricted Domains
56Logical Equivalences with Quantifiers
57Prenex Normal Form
58Set Fundamentals and Notation
59Special Sets and Set Equality
60Subsets and Proper Subsets
61Power Sets
62Set Union and Intersection
63Set Difference and Complement
64Venn Diagrams
65Set Identities and Laws
66Cartesian Products
67Relations as Sets of Ordered Pairs
68Representing Relations
69Properties of Relations: Reflexivity
70Properties of Relations: Symmetry
71Properties of Relations: Transitivity
72Equivalence Relations
73Equivalence Classes and Partitions
74Partial Orders
75Total Orders and Chains
76Definition and Notation of Functions
77Function Properties: Injective (One-to-One)
78Function Properties: Surjective (Onto)
79Function Properties: Bijective
80Composition of Functions
81Inverse Functions
82Sequence Fundamentals and Notation
83Arithmetic and Geometric Sequences
84Recurrence Relations
85Summation Notation and Series
86The Principle of Mathematical Induction
87Base Case: Starting the Proof
88Inductive Hypothesis
89Inductive Step: The Core Argument
90Summing Series by Induction
91Divisibility Proofs by Induction
92Inequality Proofs by Induction
93Strong Induction
94Structural Induction
95Common Induction Mistakes
96Well-Ordering Principle
97Induction in Algorithm Analysis
98Counting Principles: Sum and Product Rules
99Permutations: Arrangements Without Repetition
100Combinations: Selections Without Order
101Permutations with Repetition
102Combinations with Repetition (Stars and Bars)
103The Pigeonhole Principle
104Binomial Coefficients and Pascal's Triangle
105The Binomial Theorem
106Inclusion-Exclusion Principle
107Counting Problems in Computer Science

Computer Science

31Propositions and Truth Values
32Logical Negation
33Logical Conjunction (AND)
34Logical Disjunction (OR)
35Exclusive OR (XOR)
36Conditional Statements (Implication)
37Converse, Inverse, and Contrapositive
38Biconditional Statements
39Compound Propositions and Precedence
40Logical Equivalence
41De Morgan's Laws
42Distributive and Associative Laws
43Tautologies and Contradictions
44Logical Inference Rules
45Normal Forms: CNF and DNF
46Predicates and Propositional Functions
47Universal Quantifier (∀)
48Existential Quantifier (∃)
49Negating Quantified Statements
50Nested Quantifiers
51Translating English to Predicate Logic
52Translating Predicate Logic to English
53Quantifier Scope and Binding
54Uniqueness Quantifier (∃!)
55Quantifiers Over Restricted Domains
56Logical Equivalences with Quantifiers
57Prenex Normal Form
58Set Fundamentals and Notation
59Special Sets and Set Equality
60Subsets and Proper Subsets
61Power Sets
62Set Union and Intersection
63Set Difference and Complement
64Venn Diagrams
65Set Identities and Laws
66Cartesian Products
67Relations as Sets of Ordered Pairs
68Representing Relations
69Properties of Relations: Reflexivity
70Properties of Relations: Symmetry
71Properties of Relations: Transitivity
72Equivalence Relations
73Equivalence Classes and Partitions
74Partial Orders
75Total Orders and Chains
76Definition and Notation of Functions
77Function Properties: Injective (One-to-One)
78Function Properties: Surjective (Onto)
79Function Properties: Bijective
80Composition of Functions
81Inverse Functions
82Sequence Fundamentals and Notation
83Arithmetic and Geometric Sequences
84Recurrence Relations
85Summation Notation and Series
86The Principle of Mathematical Induction
87Base Case: Starting the Proof
88Inductive Hypothesis
89Inductive Step: The Core Argument
90Summing Series by Induction
91Divisibility Proofs by Induction
92Inequality Proofs by Induction
93Strong Induction
94Structural Induction
95Common Induction Mistakes
96Well-Ordering Principle
97Induction in Algorithm Analysis
98Counting Principles: Sum and Product Rules
99Permutations: Arrangements Without Repetition
100Combinations: Selections Without Order
101Permutations with Repetition
102Combinations with Repetition (Stars and Bars)
103The Pigeonhole Principle
104Binomial Coefficients and Pascal's Triangle
105The Binomial Theorem
106Inclusion-Exclusion Principle
107Counting Problems in Computer Science

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Lesson 67 of 2,872·2. Discrete Mathematics for CSPro lesson

Relations as Sets of Ordered Pairs

Define binary relations as subsets of Cartesian products; introduce domain, codomain, and range.

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