MAT 3100 Introduction to Proof

Slides:

Advertisements

Similar presentations

Inverses, Contrapositives, and Indirect Reasoning

Advertisements

Discrete Math Methods of proof 1.

Introduction to Proofs

Chapter 3 Elementary Number Theory and Methods of Proof.

Write the negation of “ABCD is not a convex polygon.”

(5-4) I NVERSES AND CONTRAPOSITIVES Learning Targets: To write the negation of a statement. To write the inverse and the contrapositive of a conditional.

Section 5-4: Indirect Reasoning March 7, Warm-up Warm-up: Practice 5-3: p. 58, 1-13.

5-4 Inverses, Contrapositives, and Indirect Reasoning

EXAMPLE 4 Prove the Converse of the Hinge Theorem

MAT 3749 Introduction to Analysis Section 0.1 Part I Methods of Proof I

So far we have learned about:

1 Indirect Argument: Contradiction and Contraposition.

Introduction to Proofs ch. 1.6, pg. 87,93 Muhammad Arief download dari

Accelerated Math I Unit 2 Concept: Triangular Inequalities The Hinge Theorem.

MAT 3749 Introduction to Analysis Section 0.2 Mathematical Induction

Methods of Proof & Proof Strategies

Introduction to Proofs

Copyright © Cengage Learning. All rights reserved. CHAPTER 4 ELEMENTARY NUMBER THEORY AND METHODS OF PROOF ELEMENTARY NUMBER THEORY AND METHODS OF PROOF.

Methods of Proofs PREDICATE LOGIC The “Quantifiers” and are known as predicate quantifiers. " means for all and means there exists. Example 1: If we.

1.1 Introduction to Inductive and Deductive Reasoning

Section 2.21 Indirect Proof: Uses Laws of Logic to Prove Conditional Statements True or False.

Logical Reasoning:Proof Prove the theorem using the basic axioms of algebra.

5-4 Inverses, Contrapositives, and Indirect Reasoning

Warm Up. Writing the negation of each statement. 1)The m

Proof By Contradiction Chapter 3 Indirect Argument Contradiction Theorems and pg. 171.

Fall 2008/2009 I. Arwa Linjawi & I. Asma’a Ashenkity 11 The Foundations: Logic and Proofs Introduction to Proofs.

1 Discrete Structures – CNS2300 Text Discrete Mathematics and Its Applications Kenneth H. Rosen (5 th Edition) Chapter 3 The Foundations: Logic and Proof,

Methods of Proof Dr. Yasir Ali. Proof A (logical) proof of a statement is a finite sequence of statements (called the steps of the proof) leading from.

DISCRETE COMPUTATIONAL STRUCTURES CSE 2353 Fall 2010 Most slides modified from Discrete Mathematical Structures: Theory and Applications by D.S. Malik.

2-6 Proving Angles Congruent. Theorem: a conjecture or statement that you prove true.

MAT 2720 Discrete Mathematics Section 2.2 More Methods of Proof Part II

Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.

MAT 2720 Discrete Mathematics Section 2.1 Mathematical Systems, Direct proofs, and Counterexamples

Bellwork Write if-then form, converse, inverse, and contrapositive of given statement. 3x - 8 = 22 because x = 10.

5-5 Indirect Proof. Indirect Reasoning: all possibilities are considered and then all but one are proved false. The remaining possibility must be true.

 You will be able to use theorems and definitions to find the measures of angles.  You will be able to use theorems and definitions to write a formal.

EXAMPLE 3 Write an indirect proof Write an indirect proof that an odd number is not divisible by 4. GIVEN : x is an odd number. PROVE : x is not divisible.

Draw a Logical Conclusion:  If you are a lefty then you struggle to use a can opener.  If you like math then you must be smart.  If you are smart then.

Analyze Conditional Statements Objectives: 1.To write a conditional statement in if-then form 2.To write the negation, converse, inverse, and contrapositive.

Section 9.4 – Mathematical Induction Mathematical Induction: A method to prove that statements involving natural numbers are true for all natural numbers.

6-3: Theorems on Lines and Planes -Indirect proof -Existence Proof -Uniqueness Proof Proof Geometry.

Chapter 1 Logic and proofs

MAT 3730 Complex Variables Section 2.4 Cauchy Riemann Equations

Chapter 1 Logic and Proof.

Indirect Argument: Contradiction and Contraposition

3. The Logic of Quantified Statements Summary

Indirect Argument: Two Classical Theorems

You will learn to use indirect reasoning to write proofs

Direct Proof by Contraposition Direct Proof by Contradiction

Math 2 Geometry Based on Elementary Geometry, 3rd ed, by Alexander & Koeberlein 2.2 Indirect Proof.

Methods of Proof A mathematical theorem is usually of the form pq

Indirect Argument: Contradiction and Contraposition

Discrete Math for CS CMPSC 360 LECTURE 4 Last time and recitations:

Check It Out! Example 1 Write an indirect proof that a triangle cannot have two right angles. Step 1 Identify the conjecture to be proven. Given: A triangle’s.

MAT 3749 Introduction to Analysis

Indirect Proof by Contradiction Direct Proof by Cases

Copyright © 2014 Pearson Education, Inc.

Class Greeting.

MAT 3100 Introduction to Proof

Sullivan Algebra and Trigonometry: Section 13.4

Dr. Halimah Alshehri MATH 151 Dr. Halimah Alshehri Dr. Halimah Alshehri.

Copyright © Cengage Learning. All rights reserved.

1.1 Introduction to Inductive and Deductive Reasoning

MAT 3100 Introduction to Proof

5.6 Inequalities in Two Triangles and Indirect Proof

6-2: Indirect Proofs Proof Geometry.

Chapter 5 Parallel Lines and Related Figures

Introduction to Proofs

Science is fun. Science is fun. Science is fun. Science is fun. Science is fun. Science is fun. Science is fun. Science is fun. Science is fun. Science.

Presentation transcript:

MAT 3100 Introduction to Proof 04 Methods of Proof II http://myhome.spu.edu/lauw

I cannot see some of the symbols! Download the trial version of MATH TYPE equation edition from design science http://www.dessci.com/en/products/mathtype/trial.asp

Preview of More Reviews Indirect Proofs Contradiction Proof by Contrapositive is considered as a special case of proof by contradiction Proof by cases Existence proofs

Proof by Contradiction Proof by Contrapositive Proof by Contradiction

Example 1 Analysis Proof

Proof by Contradiction Analysis Proof by Contradiction of If-then Theorem Suppose the negation of the conclusion is true. Find a contradiction. State the conclusion.

Proof by Contradiction The method also work with statements other then If P then Q

Example 2 Analysis Proof

Pause Here Classwork

Proof by Cases

Example 3 Analysis Proof

Proof by Cases Analysis Proof by Cases of If-then Theorem Split the domain of interest into cases. Prove each case separately. State the conclusion. Note that the cases do not have to be mutually exclusive. They just have to cover all elements in the domain.

Existence Proofs

Example 4 Analysis Proof

Existence Proofs Analysis Existence Proof Prove the statement by exhibiting an element in the domain of interest that satisfies the given conditions. State the conclusion.

Group Explorations 04 Very fun to do. Keep your voices down…you do not want to spoil the fun for the other groups.