'Indirect proof' diaporamas de présentation

Welcome To

Welcome To. Bisectors, Medians, and Altitudes. Inequalities and Triangles. The Triangle Inequality. 2 Triangles & Inequalities. Indirect Proof. $100. $100. $100. $100. $100. $200. $200. $200. $200. $200. $300. $300. $300. $300. $300. $400. $400. $400. $400. $400. $500.

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Daily Announcements

Daily Announcements. CS/APMA 202 Spring 2005 Aaron Bloomfield. Tuesday, 25 January 2005. HW 1: assigned today, due next Tue (1 Feb) Rosen, section 1.1: 18, 48, 60 HW 2: assigned Thu, due following Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50

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CSE115/ENGR160 Discrete Mathematics 02/01/11

CSE115/ENGR160 Discrete Mathematics 02/01/11. Ming-Hsuan Yang UC Merced. 1.6 Direct proofs of p?q. First assume p is true Then show q must be true (using axioms, definitions, and previously proven theorems) So the combination of p is true and q is false never occurs Thus p?q is true

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Methods of Proof

Methods of Proof. CS/APMA 202 Epp, chapter 3 Aaron Bloomfield. Proof methods. We will discuss ten proof methods: Direct proofs Indirect proofs Vacuous proofs Trivial proofs Proof by contradiction Proof by cases Proofs of equivalence Existence proofs Uniqueness proofs Counterexamples.

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Discrete Structures Introduction to Proofs

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Methods of Proof

Methods of Proof. CS/APMA 202 Epp, chapter 3 Aaron Bloomfield. Proof methods. We will discuss ten proof methods: Direct proofs Indirect proofs Vacuous proofs Trivial proofs Proof by contradiction Proof by cases Proofs of equivalence Existence proofs Uniqueness proofs Counterexamples.

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Discrete Mathematics, Part II CSE 2353 Fall 2007

Discrete Mathematics, Part II CSE 2353 Fall 2007. Margaret H. Dunham Department of Computer Science and Engineering Southern Methodist University Some slides provided by Dr. Eric Gossett; Bethel University; St. Paul, Minnesota

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Journal chapter 5

Journal chapter 5 . By: maria jose diaz-duran. Describe what a perpendicular bisector is. Explain the perpendicular bisector theorem and its converse. Perpendicular Bisector: is a line perpendicular to a segment at its midpoint.

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Chapter 5 Review

Chapter 5 Review. Segments in Triangles. Test Outline. Multiple Choice Be able to identify vocab (pick out from a picture) Be able to apply SAS and SSS Inequality Theorems (biggest angle across from biggest side)

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Chap 3

Chap 3. A theorem is a statement that can be shown to be true A proof is a sequence of statements to show that a theorem is true Axioms: statements which are assumptions, hypotheses or previously proved theorem Pales of inference: draw conclusion from other assertions. Chap 3 (cont.).

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Proving Existentials

Proving Existentials. A proof of a statement of the form ? x P ( x ) is called an existence proof . If the proof demonstrates how to actually find or construct a specific element a such that P ( a ) is true, then it is a constructive proof. Otherwise, it is nonconstructive .

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Negation Rules

Negation Rules. Reductio Ad Adsurdum Indirect Proof Dash In and Dash Out. Negation Rules. Reductio Ad Adsurdum Indirect Proof Dash In and Dash Out The basic idea: To prove A, Assume -A and derive a contradiction. Since -A leads to a contradiction, -A must be wrong,

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The Foundations: Logic and Proofs

The Foundations: Logic and Proofs. Introduction to Proofs. 1. Some terminology. Theorem : is a statement that can be shown to be true. Axioms (postulates): Statements that used in a proof and are assumed to be true. Proof Methods Proving p ? q

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Lecture 11

Lecture 11. 1.5, 3.1 Methods of Proof. Last time in 1.5. To prove theorems we use rules of inference such as: p, p ?q, therefore, q NOT q, p?q, therefore NOT p. p AND q, therefore p FORALL x P(x), therefore for arbitrary c, P(c) EXISTS x P(x), therefore for some c, P(c)

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Advanced Geometry 5.1

Advanced Geometry 5.1. Indirect proof. 2-Column Proof Form: 2-column format Begin with the GIVEN statements Goal: Prove a statement directly. Indirect Proof Form: Paragraph form Begin with the PROVE statement Goal: Achieve a contradiction of an assumption to complete the proof.

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The Null Hypothesis

The Null Hypothesis. Modus Tollens* : The Logic of the Null Hypothesis

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5-5 Indirect Proof

5-5 Indirect Proof. Fun Geometry Logic with DLB. Writing an Indirect Proof. Temporarily assume the opposite of what you are trying to prove. Reason directly until you find a contradiction of a known fact.

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