MATH 112 • Discrete Mathematics • Midterm I

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Ders Tanıtımı

Introduction

Negation of a Proposition

Conjunction

Disjunction

Conditional Statement

BiConditional Statement

Exclusive OR

Truth Table

Example 1

Example 2

Example 3

Example 4

Example 5

Tautology

Example 1

Contradiction

Converse Inverse Contrapositive

Example

Exam-like Question

Logical Equivalences

Logical Equivalences

De Morgan Example

Example

Example

Example

Example

Example

Exam-like Question

Exam-like Question

Exam-like Question

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Example

Example

Example

Example

Example

Example

Nested Quantifiers

Example

Example

Example

Example

Example

Example

Negation of Nested Quantifiers

Example

Example

Translations

Example

Example

Example

Example

Example

Translation of Mathematical Statements

Translation of Statements With Multiple Variables

Example

Example

Example

Example

Example

Example

Example

Example

Logic Puzzle

Logic Puzzle

Arguments

Example

Direct Proof

Ücretsiz

Example 1

Ücretsiz

Example 2

Example 3

Example 4

Example 5

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Exam-like Question 5

Proof By Cases

Example 1

Example 2

Example 3

Example 4

Example 5

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Existence Proof

Example 1

Example 2

Existence and Uniqueness Proof

Example 1

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Contrapositive Proof

Example 1

Example 2

Example 3

Example 4

Example 5

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Proof by Counterexample

Example 1

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Proof by Contradiction

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Exam-like Question 5

If and Only if Statements

Example 1

Example 2

Example 3

Example 4

Example 5

Exam-like Question 1

Exam-like Question 2

Direct Proof

Example 1

Example 2

Example 3

Example 4

Example 5

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Exam-like Question 5

Proof By Cases

Example 1

Example 2

Example 3

Example 4

Example 5

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Existence Proof

Example 1

Example 2

Existence and Uniqueness Proof

Example 1

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Contrapositive Proof

Example 1

Example 2

Example 3

Example 4

Example 5

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Proof by Counterexample

Example 1

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Proof by Contradiction

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

Exam-like Question 5

If and Only if Statements

Example 1

Example 2

Example 3

Example 4

Example 5

Exam-like Question 1

Exam-like Question 2

Introduction

Ücretsiz

Proof of Formulas by Induction

Ücretsiz

Example 1

Example 2

Example 3

Example 4

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Exam-like Question 4

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

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

Introduction to Counting

Exam like Question 6

Exam like Question 7

Combination & Permutation: Intuition

Exam like Question 8

Exam like Question 9

Combination

Exam like Question 10

Exam like Question 11

Exam like Question 12

Exam like Question 13

Permutation 1

Permutation 2

Exam like Question 14

Exam like Question 15

Exam like Question 16

Binomial Theorem

Example 1

Example 3

Example 2

Pascal Identity

Vandermonde's Identity

Example 1

Combinatorial Proof

Example 1

Principle Inclusion-Exclusion

Example 1

Example 2

Distributing Objects into Boxes

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Eğitmen

İhsan Altundağİhsan Altundağ
Eğitmen

2007 yılında Galatasaray Üniversitesi Bilgisayar Mühendisliği bölümünden birincilikle mezun olduktan sonra Fransa'da Kriptoloji üzerine Fransa hükümeti tarafından verilen bursla yüksek lisans yaptım. Devamında ikinci kez sınava girerek Boğaziçi Matematik bölümünü de bitirdim. Yaklaşık 15 yıldır üniversite öğrencilerine dersler vermekteyim.

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