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 1

Direct Proof 2

Direct Proof 3

Direct Proof 4

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contradiction 1

Proof by Contradiction 2

Proof by Cases

Proofs of Equivalence

Induction for Formulas 1

Induction for Formulas 2

Induction for Formulas 3

Induction for Formulas 4

Induction Proof for Divisibility 1

Induction Proof for Divisibility 2

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 Relation

Example 12

Example 13

Reflexive Relations

Example 14

Symmetric Relations

Antisymmetric Relations

Example 15

Transitive Relations

Properties of Relations

Example 16

Composition of Relations

Equivalence Relation

Example 17

Partial Ordering

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

Proofs & Sets 1

Proofs & Sets 2

Proofs & Sets 3

Proofs & Sets 4 (i ve j ŞIKLARI HARİÇ)

Functions 1

Functions 2

Functions 3

Functions 4

Function & Summation (SADECE 2. ve 3. SORULAR)

Functions & Sets

Functions & Sets & Summation (4. ŞIK HARİÇ)

Functions & Summation

Relations 1

Relations 2

Relations 3

Relations 4

Relations 5

Definition of Divisibility

Example 1

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

GCD Greatest Common Divisor

LCM Least Commun Multiple

Euclidian Algorithm

Example 1

Bézout Identity

Example 1

Example 2

Affine Cipher

Example 1

Example 2

Transposition Cipher

RSA Algorithm

Example 1

Example 2

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Identical Objects Example 2

Identical Objects Example 3

Combination

n choose r

Committee Example 1

Committee Example 2

Ball Example 1

Ball Example 2

Number Theory 1

Number Theory 2

Number Theory 3

RSA Algorithm 1

RSA Algorithm 2

RSA Algorithm 3

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6