CMPE 201 • Midterm • Discrete Computational 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

Valid Argument

Rules of Inferences

Example 1

Example 2

Example 3

Using Rules of Inferences to Build Arguments

Example 4

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

Truth Table & Tautology

Logical Equivalences

Logical Equivalences

Logical Equivalences

Tautology

Quantifiers

Quantifiers

Quantifiers

Nested Quantifiers

Nested Quantifiers

Translations

Translations

Translations

Rules of Inferences 1

Rules of Inferences 2

Rules of Inferences 3

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

Definition and Notation

Subset

Example

Union and Intersection of Two Sets

Difference of Two Sets

Set Identities

Example

Power Set

Example

Cartesian Product

Example 1

Example 2

Proof Example 1

Proof Example 2

Definition of Sequence

Arithmetique Sequence

Example

Geometric Sequence

Example

Sum Notation

Example

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Example 3

Example 4

Proof of Divisibility by Induction

Example 1

Example 2

Proof of Inequality by Induction

Example 1

Example 2

Induction Related to Fibonacci

Strong Induction

Introduction

Recursively Defined Functions

Example 1

Recursively Defined Sets

Example 2

Recursively Defined Strings

Example 3

Structural Induction

Example 4

Example 5

Sets 1

Sets 2

Sets 3

Sets 4 ( i ve j ŞIKLARI HARİÇ)

Summation (SADECE 2. SORU)

Summation (SADECE 2. SORU)

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

Recursion and Induction

Recursive Algorithm