Lecture 3 Proofs Pdf Theorem Axiom Chapter 4 proofs. by: aaron friedman heiman and david oliver. asa angle side angle. used to prove triangle congruence: if two angles and the included side of two triangles are congruent, then the triangles are congruent. given: kl and no are parallel; m bisects ko. It introduces truth tables to assess validity and identifies common valid argument forms like modus ponens and modus tollens. the document also discusses direct proofs, proof by cases, and other proof techniques in discrete mathematics. download as a pptx, pdf or view online for free.
Chap4 Proofs Pdf Mathematical Proof Theorem Transcript and presenter's notes title: chapter 4: propositional proofs 1 chapter 4 propositional proofs. Section 4.1 proofs involving divisibility of integers in general, for integers a and b with a≠0, we say that a divides b if there is an integer c such that b=ac. in this case, we write a | b. if a | b, then we also say that b is a multiple of a and that a is a divisor of b. Document 4. proofs.ppt, subject mathematics, from north south university, length: 27 pages, preview: methods of proof this lecture now we have learnt the basics in logic. we are going to apply. We will rotate through 4 stations to fill out proofs you will have approximately 4 minutes per station. work quickly but accurately! warm up 4.5 isosceles and equilateral triangles learning targets i can use properties of isosceles triangles. i can use properties of equilateral triangles.
Proofs Of Section 4 3 Pdf Calculus Mathematical Objects Document 4. proofs.ppt, subject mathematics, from north south university, length: 27 pages, preview: methods of proof this lecture now we have learnt the basics in logic. we are going to apply. We will rotate through 4 stations to fill out proofs you will have approximately 4 minutes per station. work quickly but accurately! warm up 4.5 isosceles and equilateral triangles learning targets i can use properties of isosceles triangles. i can use properties of equilateral triangles. Case 1: (m=n) → (m2=n2) (m)2 = m2, and (n)2 = n2, so this case is proven case 2: (m= n) → (m2=n2) (m)2 = m2, and ( n)2 = n2, so this case is proven (m2=n2) → [(m=n) (m= n)] subtract n2 from both sides to get m2 n2=0 factor to get (m n)(m n) = 0 since that equals zero, one of the factors must be zero thus, either m n=0 (which means m=n) or m n=0 (which means m= n) existence proofs given a statement: x p(x) we only have to show that a p(c) exists for some value of c two types: constructive: find a specific value of c for which p(c) exists nonconstructive: show that such a c exists, but don’t actually find it assume it does not exist, and show a contradiction constructive existence proof example show that a square exists that is the sum of two other squares proof: 32 42 = 52 show that a cube exists that is the sum of three other cubes proof: 33 43 53 = 63 non constructive existence proof example rosen, section 1.5, question 50 prove that either 2*10500 15 or 2*10500 16 is not a perfect square a perfect square is a square of an integer rephrased: show that a non perfect square exists in the set {2*10500 15, 2*10500 16} proof: the only two perfect squares that differ by 1 are 0 and 1 thus, any other numbers that differ by 1 cannot both be perfect squares thus, a non perfect square must exist in any set that contains two numbers that differ by 1 note that we didn’t specify which one it was!. Overview of §1.5 methods of mathematical argument (i.e., proof methods) can be formalized in terms of rules of logical inference. mathematical proofs can themselves be represented formally as discrete structures. we will review both correct & fallacious inference rules, & several proof methods. These power points take you through each chapter of the course and provide some handy hints along the way!. This document contains a lecture on mathematical proofs. it discusses: 1) the difference between examples and proofs, with proofs needing to use general properties rather than specific cases.
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