Outline •What is a Proof ? Next Page . The argument is valid if the premises imply the conclusion.An argument form is an argument that is valid no matter what propositions are substituted into its propositional variables. Suppose we want to prove the following statement: The number 7 is a rational number. Discrete Mathematics Lecture 4 Proofs: Methods and Strategies 1 . Besides the importance of logic in understanding mathematical reasoning, logic has many applications to computer science. P (k) → P (k + 1). Previous Page. Discrete Mathematics - Propositional Logic. Because a major goal of this Website is to teach the reader how to understand and how to construct correct mathematical arguments, we begin our study of discrete mathematics with an introduction to logic. Introduction to Proofs. Ex 2.1.1 The sum of two even numbers is even. In 1-4, write proofs for the given statements, inserting parenthetic remarks to explain the rationale behind each step (as in the examples). The next step in mathematical induction is to go to the next element after k and show that to be true, too:. Arguments in Propositional Logic A argument in propositional logic is a sequence of propositions.All but the final proposition are called premises.The last statement is the conclusion. The rules of mathematical logic specify methods of reasoning mathematical statements. Okay, now that we understand direct and indirect proofs, let's get a bit more mathematical. • Direct proof • Contrapositive • Proof by contradiction • Proof by cases 3. Math 3336 Section 1. Discrete Math Lecture 03: Methods of Proof 1. Direct Proof (Example 2) •Show that if m and n are both square numbers, then m n is also a square number. Ex 2.1.2 The sum of an even number and an odd number is odd. You have proven, mathematically, that everyone in the world loves puppies. We are going to apply the logical rules in proving mathematical theorems. Topics: Mathematical Proofs Forms of Theorems Direct Proofs Indirect Proofs Proof of the Contrapositive Proof by Contradiction Mistakes in Proofs. Proof by contraposition is a type of proof used in mathematics and is a rule of inference. Definition: A theorem is a statement that can be shown to be true. Greek philosopher, Aristotle, was the pioneer of logical reasoning. •Proof : Assume that m and n are both squares. This Lecture Now we have learnt the basics in logic. If you can do that, you have used mathematical induction to prove that the property P is true for any element, and therefore every element, in the infinite set. Advertisements. Methods of Proof Lecture 3: Sep 9 2. This

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