MATH 250 • Midterm I • Discrete Mathematics for Engineering

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Exam like Question 1

Tautology

Exam like Question 2

Contradiction

Converse Inverse Contrapositive

Exam like Question 3

Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

Exam like Question 4

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Exam like Question 5

Nested Quantifiers

Exam like Question 6

Negation of Nested Quantifiers

Exam like Question 7

Translations

Exam like Question 8

Exam like Question 9

Translation of Statements With Multiple Variables

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 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 10

Geometric Sequence

Example 11

Sum Notation

Example 12

Definition of Relation

Example 1

Example 2

Example 3

Example 4

Reflexive Relations

Example 5

Example 6

Symmetric Relations

Antisymmetric Relations

Example 7

Transitive Relations

Example 8

Properties of Relations

Example 9

Example 10

Equivalence Relation

Example 11

Example 12

Sets 1

Sets 2

Sets 3

Sets 4

Sets 5

Functions 1

Functions 2

Functions 3

Functions 4

Functions 5

Sets & Function

Properties of Relation

Properties of Relation

Equivalence Relation 1

Equivalence Relation 2

Equivalence Relation 3

Equivalence Relation 4

What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Exam Like Question 1

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Insertion Sort Algorithm

Insertion Sort Algorithm - Code

Big-O Notation

Example 1

Example 2

Example 3

Example 4

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

Example 1

Example 2

Big-Omega Notation

Big-Theta Notation

Example 1

Example 2

Definition of Divisibility

Example 1

Example 2

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

Example 2

Prime Numbers

Example 1

Example 2

GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

Euclidian Algorithm

Example 1

Bezout Identity

Example 1

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Exam-like Question 1

Exam-like Question 2

Proof of Divisibility by Induction

Example 1

Example 2

Exam-like Question 1

Exam-like Question 2

Proof of Inequality by Induction

Example 1

Example 2

Example 3

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Induction Related to Fibonacci

Exam-like Question 1

Strong Induction

Example 1

Growth of Functions 1

Growth of Functions 2

Growth of Functions 3

Growth of Functions 4

Algorithms 1

Algorithms 2

Algorithms 3

Number Theory 1

Number Theory 2

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 1

Induction for Inequalities 2

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Counting 7

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3