PPT-Methods of Proof

This Lecture Now we have learnt the basics in logic We are going to apply the logical rules in proving mathematical theorems Direct proof Contrapositive Proof by contradiction Proof by cases. They are motivated by the dependence of the Taylor methods on the speci64257c IVP These new methods do not require derivatives of the righthand side function in the code and are therefore generalpurpose initial value problem solvers RungeKutta metho The basic idea is to assume that the statement we want to prove is false and then show that this assumption leads to nonsense We are then led to conclude that we were wrong to assume the statement was false so the statement must be true As an examp U-Prove Revocation. Tolga . Acar. , Intel. Sherman S.M. Chow. , The Chinese University of Hong Kong. Lan Nguyen. , XCG – Microsoft Research. Outline. Accumulators. Definitions. . and Security. Anonymous Revocation. Ken McMillan. Microsoft Research. Aws Albarghouthi. University of Toronto. Generalization. Interpolants. are . generalizations. We use them as a way of forming conjectures and lemmas. Many . proof search methods uses . Yeting. . Ge. Clark Barrett. SMT . 2008. July 7 Princeton. SMT solvers are more complicated. CVC3 contains over 100,000 lines of code. Are SMT solvers correct?. . Quest for . correct. SMT solvers?. Inquiries into the Philosophy of Religion. A Concise Introduction. Chapter 5. God And Morality. By . Glenn Rogers, Ph.D.. Copyright. ©. 2012 . Glenn Rogers. Proof of God?. God and Morality. Aristotle referred to man (humankind) as the rational animal, emphasizing that it is human rationality that sets humans apart from animals. . U-Prove Revocation. Tolga . Acar. , Intel. Sherman S.M. Chow. , The Chinese University of Hong Kong. Lan Nguyen. , XCG – Microsoft Research. Outline. Accumulators. Definitions. . and Security. Anonymous Revocation. Statutory . Burden -- EC . § . 256.152. Applicant must prove testator did not revoke the will.. How prove a negative?. Presumption of Non-Revocation. Ashley v. Usher. – p. . 187. Source . of will “normal”. 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. To prove an argument is valid or the conclusion follows . Basic . definitions:Parity. An . integer. n is called . even. . if, and only if. , . there exists . an integer k such that . n = 2*k. .. An integer n is called . odd. if, and only if, . it is not even.. Basic . definitions:Parity. An . integer. n is called . even. . if, and only if. , . there exists . an integer k such that . n = 2*k. .. An integer n is called . odd. if, and only if, . it is not even.. Probabilistic Proof System — An Introduction Deng Yi CCRG@NTU A Basic Question Suppose: You are all-powerful and can do cloud computing (i.e., whenever you are asked a question, you can give the correct answer in one second by just looking at the cloud overhead) — . An Introduction. Deng. . Yi. CCRG@NTU. A Basic Question. Suppose:. You are all-powerful and can do cloud computing (i.e., whenever you are asked a question, you can give the correct answer in one second by just looking at the cloud overhead). Now we have learnt the basics in logic.. We are going to apply the logical rules in proving mathematical theorems.. Direct proof. Contrapositive. Proof by contradiction. Proof by cases. Basic Definitions.