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Trivial Proofs - Discrete Mathematics and its Applications - Lecture Slides

Slides, Discrete Mathematics

Post: April 27th, 2013
Description
During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Trivial Proofs, Methods of Proof, Rules of Inference, Proof Strategies, Vacuous Proofs, Empty Set, Postive Integers, Example Indirect Proof, Proof by Contradiction, Common Divisor, Equivalence Proofs, Theorems with Quantifiers
During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Trivial Proofs, Methods of Proof, Rules of Inference, Proof Strategies, Vacuous Proofs, Empty Set, Postive Integers, Example Indirect Proof, Proof by Contradiction, Common Divisor, Equivalence Proofs, Theorems with Quantifiers
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Lecture 11 1.5, 3.1 Methods of Proof Docsity.com 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) It is easy to make mistakes, make sure that: 1) All premises pi are true when you prove (p1 AND p2 AND...pn)  q 2) Every rule of inference you use is correct. Some proof strategies: To proof pq 1) direct proof: assume p is true, use rules to prove that q is true. 2) indirect proof, assume q is NOT true, use rules to prove p is NOT true. To prove p is true: 3) By contradiction: assume p is NOT true, use rules to show that NOT pF i.e. it leads to a contradiction. Docsity.com Vacuous –Trivial Proofs Lets say we want to prove pq but the premise p can be shown to be false! Then pq is always true because (FT) = T and (FF) = T. This is a vacuous prove. Old example: prove that for any se..

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