COMP 106 • Midterm • Discrete Mathematics for Computer Science and Engineering

Introduction

Negation of a Proposition

Compound Proposition

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

Exam like Question 10

Exam like Question 11

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Nested Quantifiers

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Negation of Nested Quantifiers

Translations

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

Translation of Mathematical Statements

Translation of Statements With Multiple Variables

Exam like Question 15

Exam like Question 16

Exam like Question 17

Exam like Question 18

Exam like Question 19

Exam like Question 20

Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Logic Basics 5

Logic Basics 6

Quantifiers 1

Quantifiers 2

Quantifiers 3

Quantifiers 4

Quantifiers 5

Translation 1

Translation 2

Translation 3

Translation 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

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

Injective Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Surjective Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Bijective Function

Image of a Set

Example 1

Proof Example For Image of a Function

Preimage of a Set

Example 1

Example 2

Proof Example for Preimage of a Function

Example 1

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

Example 11

Composition of Relations

Example 12

Example 13

Combining Relations

Inverse and Complementary of a Relation

Example 14

Matrix Representation of a Relation 1

Matrix Representation of a Relation 2

Example 15

Operations on Zero - One Matrices

Example 16

Reflexive Closure

Symmetric Closure

Example 17

Transitive Closure & Connectivity Relation

Matrix Representation of Transitive Closure

Example 18

Equivalence Relation

Example 19

Example 20

Example 21

Example 22

Example 23

Example 24

Partially Ordered Set

Example 25

Example 26

Proofs & Sets 1

Proofs & Sets 2

Proofs & Sets 3

Proofs & Sets 4

Sets and Function 1

Relations 1

Relations 2

Relations 3

Relations 4

Relations 5

Relations 6

Relations 7

Relations 8

Relations 9

Logic : Quantifiers 1

Logic : Quantifiers 2

Logic : Quantifiers 3

Logic : Quantifiers 4