CE 215 • Midterm • Discrete Mathematics for Computer Science

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Exam like Question 1

Exam like Question 2

Tautology

Exam like Question 3

Contradiction

Converse Inverse Contrapositive

Exam like Question 4

Exam-like Question 5

Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

Exam like Question 6

Exam like Question 7

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Exam like Question 1

Nested Quantifiers

Exam like Question 2

Exam like Question 3

Negation of Nested Quantifiers

Exam like Question 4

Exam like Question 5

Translations

Exam like Question 6

Exam like Question 7

Exam like Question 8

Translation of Statements With Multiple Variables

Exam like Question 9

Exam like Question 10

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

Example 4

Proof by Contrapositive

Example 1

Example 2

Example 3

Proof by Contradiction

Example 1

Example 2

Proof by Counterexample

Example 1

Proof By Cases

Example 1

Example 2

Example 3

Proofs of Equivalence

Example 1

Example 2

Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Logic Basics 5

Logic: Quantifiers 1

Logic: Quantifiers 2

Logic: Quantifiers 3

Logic - Quantifiers 4

Logic - Quantifiers 5

Logic - Quantifiers 6

Logic - Translation 1

Logic - Translation 2

Logic - Translation 3

Logic - Translation 4

Logic - Translation 5

Rules of Inferences 1

Rules of Inferences 2

Rules of Inferences 3

Direct Proof 1

Direct Proof 2

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contradiction 1

Proof by Contradiction 2

Proof by Contradiction 3

Proof by Contradiction 4

Proof by Contradiction 5

Proof by Cases 1

Proofs of Equivalence 1

Proofs of Equivalence 2

Definition and Notation

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

Example 5

Proof Example 1

Proof Example 2

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Definition of Function

Example 1

Number of Functions

Injective Functions

Example 2

Example 3

Example 4

Number of Injective Functions

Surjective Functions

Example 5

Example 6

Example 7

Bijective Function

Inverse Function

Example 8

Example 9

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

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

Sets 1

Sets 2

Sets 3

Sets 4

Sets 5

Sets 6

Cardinality 1

Cardinality 2

Cardinality 3

Cardinality 4

Functions 1

Functions 2

Functions 3

Functions 4

Functions 5

Sets & Function 1

Sets & Function 2

Sets & Function 3

Sets & Function 4

Sets, Function & Summation 1

Sets, Function & Summation 2

Summation and Function

All Midterm Subjects 1

All Midterm Subjects 2

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Cardinality

Binary & Octal & Hexadecimal Expansions

Summation & Recurrence Relations

Proof by Contradiction

Logical Equivalence

Valid Argument

Nested Quantifiers

Proof of Equivalence

Functions & Quantifiers

Translation

Functions

Functions

Functions

Number Theory

Number Theory

Rules of Inferences

Functions