'Constructive existence proof' diaporamas de présentation

Module #10: Proof Strategies

University of Florida Dept. of Computer & Information Science & Engineering COT 3100 Applications of Discrete Structures Dr. Michael P. Frank. Slides for a Course Based on the Text Discrete Mathematics & Its Applications (5 th Edition) by Kenneth H. Rosen. Module #10: Proof Strategies.

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Module #10: Proof Strategies

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Yonsei Univ. at Wonju Dept. of Mathematics ???? Discrete Mathematics Prof. Gab-Byung Chae

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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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CSE115/ENGR160 Discrete Mathematics 02/07/12

CSE115/ENGR160 Discrete Mathematics 02/07/12. Ming-Hsuan Yang UC Merced. Without loss of generality (WLOG). In proof, sometimes we can apply the same argument for different cases x?0, y<0: xy<0 |xy|=-xy=x(-y)=|x||y| x<0, y ?0:xy<0 |xy|=-xy=(-x)y=|x||y|

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Chapter 1: The Foundations: Logic and Proofs

Chapter 1: The Foundations: Logic and Proofs. 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy. We wish to establish the truth of ? xP ( x ) .

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