COMP 106 (Fall 23) • Discrete Mathematics for Computer Science and Engineering • Midterm

Introduction

Negation of a Proposition

Conjunction

Disjunction

Conditional Statements : IF

BiConditional : If and only If

Exclusive OR

Truth Table 1

Truth Table 2

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Tautology

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Contradiction

Converse Inverse Contrapositive

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Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

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Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

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Nested Quantifiers

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Negation of Nested Quantifiers

Translations

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Translation of Mathematical Statements

Translation of Statements With Multiple Variables

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Logic Puzzle

Logic Puzzle 2

Direct Proof

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Contrapositive Proof

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Proof by Contradiction

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Proof by Counterexample

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Existence Proof

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Existence and Uniqueness Proof

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If and Only if Statements

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What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Algorithm and Pseudocode 3

Algorithm and Pseudocode 4

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Big-O Notation

Example 1

Example 4

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

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Example 2

Big-Omega Notation

Big-Theta Notation

Example 1

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Introduction

Proof of Formulas by Induction

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Example 2

Example 3

Example 4

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Proof of Divisibility by Induction

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Example 2

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Proof of Inequality by Induction

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Example 3

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Induction Related to Fibonacci

Strong Induction

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Problem 22

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