• Direct proof • Contrapositive • Proof by contradiction • Proof by cases 3. •Proof : Assume that m and n are both squares. Next Page .
This Lecture Now we have learnt the basics in logic. Discrete Mathematics - Propositional Logic. Methods of Proof Lecture 3: Sep 9 2. Definition: A theorem is a statement that can be shown to be true. Besides the importance of logic in understanding mathematical reasoning, logic has many applications to computer science. Discrete Math Lecture 03: Methods of Proof 1.
Outline •What is a Proof ? Greek philosopher, Aristotle, was the pioneer of logical reasoning.
Suppose we want to prove the following statement: The number 7 is a rational number. The rules of mathematical logic specify methods of reasoning mathematical statements. Proof by contraposition is a type of proof used in mathematics and is a rule of inference.
Ex 2.1.2 The sum of an even number and an odd number is odd. Introduction to Proofs. Math 3336 Section 1. This Direct Proof (Example 2) •Show that if m and n are both square numbers, then m n is also a square number. Okay, now that we understand direct and indirect proofs, let's get a bit more mathematical. Advertisements. You have proven, mathematically, that everyone in the world loves puppies. 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. In 1-4, write proofs for the given statements, inserting parenthetic remarks to explain the rationale behind each step (as in the examples).
Previous Page. P (k) → P (k + 1). 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. Topics: Mathematical Proofs Forms of Theorems Direct Proofs Indirect Proofs Proof of the Contrapositive Proof by Contradiction Mistakes in Proofs. Discrete Mathematics Lecture 4 Proofs: Methods and Strategies 1 . 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. We are going to apply the logical rules in proving mathematical theorems.
Ex 2.1.1 The sum of two even numbers is even. 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.
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