COM 3013 • Midterm • Discrete Structures

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Tautology

Contradiction

Converse Inverse Contrapositive

Practice Problem 1

Practice Problem 2

Logical Equivalences 1

Logical Equivalences 2

De Morgans' Law

Example 1

Practice Problem 3

Practice Problem 4

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Example 2

Nested Quantifiers

Example 3

Negation of Nested Quantifiers

Example 4

Translations

Example 5

Example 6

Translation of Statements With Multiple Variables

Direct Proof

Example 1

Example 2

Example 3

Proof by Contrapositive

Example 4

Proof by Contradiction

Example 5

Proof By Cases

Example 6

Proofs of Equivalence

Example 7

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Proof of Divisibility by Induction

Example 3

Proof of Inequality by Induction

Example 4

Induction Related to Fibonacci

Truth Table & Tautology

Logical Equivalences

Logical Equivalences

Logical Equivalences

Tautology

Quantifiers

Quantifiers

Quantifiers

Nested Quantifiers

Nested Quantifiers

Translations

Translations

Translations

Direct Proof

Direct Proof

Direct Proof

Direct Proof

Proof by Contrapositive

Proof by Contrapositive

Proof by Contradiction

Proof by Contradiction

Proof by Cases

Induction for Formulas

Induction for Formulas

Induction for Formulas

Induction for Formulas

Induction Proof for Divisibility

Induction Proof for Divisibility

Induction for Inequalities

Induction with Fibonacci

Definition and Notation of a Set

Subset

Example 1

Union and Intersection of Two Sets

Difference of Two Sets

Set Identities

Example 2

Power Set

Example 3

Cartesian Product

Example 4

Proof Example 1

Definition of Function

Example 5

Number of Functions

Injective Functions

Example 6

Example 7

Number of Injective Functions

Surjective Functions

Example 8

Example 9

Bijective Function

Inverse Function

Example 10

Example 11

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

Sets

Sets (i ve j HARİÇ)

Sets Proof

Sets Proof

Set Proof

Functions

Functions

Functions

Functions

Functions

Functions

Functions & Quantifiers

Sets & Functions

Sets & Functions

Sets & Functions

Functions & Summation

Function & Summation (1. ŞIK HARİÇ)

Functions & Sets & Summation (4. ŞIK HARİÇ)

Definition of Divisibility

Example 1

Example 2

Example 3

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

Example 2

GCD Greatest Common Divisor

LCM Least Commun Multiple

Euclidian Algorithm

Example 1

Bézout Identity

Example 1

Example 2

Example 3

Inverse of a Number in Modular Arithmetic

Fermat's Little Theorem

Solving Linear Congruences

Example 1

Example 2

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

Euclidian Algorithm

Euclidian Algorithm & Bezout Theorem

Euclidian Algorithm & Bezout Theorem

Euclidian Algorithm & Bezout Theorem

Euclidian Algorithm & Multiplicative Inverse

Euclidian Algorithm & Multiplicative Inverse

Euclidian Algorithm & Bezout Theorem

Modular Arithmetic- True False

Modular Arithmetic

Modular Arithmetic

Solving Congruences

Solving Congruences

Solving Congruences

Solving Congruences

Bezout & Inverse & Solving Congruences

Chinese Remainder Theorem

Chinese Remainder Theorem

Chinese Remainder Theorem

Chinese Remainder Theorem