Search results with tag "Counterexample"
Proving Algorithm Correctness - Northeastern University
course.ccs.neu.edu11.3.1 Proof by Counterexample De nition 11.1 (Proof by Counterexample) Used to prove statements false, or algorithms either in-correct or non-optimal Examples: Counterexample Prove or disprove: dx+ ye= dxe+ dye. { Proof by counterexample: x = 1 2 and y = 1 2 Prove or disprove: \Every positive integer is the sum of two squares of integers"
Mathematical Proofs: Where to Begin And How to Write Them
www.hamilton.eduIn a direct proof, the first thing you do is explicitly assume that the hypothesis is true for your selected variable, ... To disprove a universally quantified statement, it suffices to find one, specific counterexample. The simpler the counterexample, the better!
Section 3.1: Direct Proof and Counterexample 1
faculty.up.eduSection 3.1: Direct Proof and Counterexample 1 In this chapter, we introduce the notion of proof in mathematics. ... is rational, then x is rational”. Disprove this statement by giving a counter example. ... (ii) Start the proof by supposing that x is a particular, but arbi-trary chosen element of D for which P(x) is true.
SECTION 4.2 Direct Proof and Counterexample II: Rational ...
storm.cis.fordham.eduDirect Proof and Counterexample II: Rational Numbers Sums, differences, and products of integers are integers. ... Deriving New Mathematics from Old. Example 4 – The Double of a Rational Number Derive the following as a corollary of Theorem 4.2.2. !!!!
1.3 — Counterexamples and Invalidity - Texas A&M University
phil240.tamu.edusubstitution instance whose premises are obviously true and whose conclusion is obviously false. So, 1. If Ryan is a pop-culture buff, then he reads Entertainment Weekly. 2. Ryan reads Entertainment Weekly. 3. Ryan is a pop-culture buff. Modus Ponens So, 1. If A, then B. 2. A. 3. B. Fallacy of Affirming the Consequent So, 1. If A, then B. 2. B ...
1.7 Introduction to Proofs - University of Hawaiʻi
courses.ics.hawaii.eduTo disprove this this proposition, we will find a counterexample. We know that p 2 is irrational. So by taking the product of p 2 and p 2, we obtain 2. 2 is a rational number from the product of two irrational numbers, thus we have disproven the statement. 1.7 pg 91 # 1 Use a direct proof to show that the sum of two odd integers is even.
K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH …
www.deped.gov.ph2. key methods of proof and disproof. 2. appropriately apply a method of proof and disproof in real-life situations. 50. illustrates the different methods of proof (direct and indirect) and disproof (indirect and by counterexample). M11GM-IIj-1 51. justifies mathematical and real-life statements using the different methods of proof and disproof.
MATH208: DISCRETE MATHEMATICS - University of North …
arts-sciences.und.edu7 Styles of Proof 69 7.1 Direct proof 69 7.2 Indirect proof 72 7.3 Proof by contradiction 72 7.4 Proof by cases 74 7.5 Existence proof 75 7.6 Using a counterexample to disprove a statement 75 7.7 Exercises 77
Introducing Parliamentary Debate - CHSSA
www.chssa.orgargument or counterexample) or question to the speaker. If the speaker refuses the point (for ... team provides a proof of the motion for debate using a specific case or a set of cases to present ... this through a combination of direct and indirect refutation of the proposition team’s case.
Introduction to Automata Theory - Washington State University
eecs.wsu.edun Logical progression by direct implications ... “proof by example”! n So when asked to prove a claim, an example that satisfied that claim is nota proof . 23 Different ways of saying the same ... counterexample n If and only if n Read chapter 1 for more examples and exercises.
BASIC CONCEPTS OF LOGIC - UMass
courses.umass.eduDemonstrating Invalidity Using the Method of Counterexamples.....13 9. Examples of Valid Arguments in Syllogistic Logic.....19 10. Exercises for Chapter 1.....22 11. Answers to Exercises for Chapter 1.....25. 2 Hardegree, Symbolic Logic ...
counterexamples - Millersville University of Pennsylvania
sites.millersville.edudivisible by 4, but n = 6 is not divisible by 4. Thus, n = 6 is a counterexample to the statement. On the other hand, consider n = 5. While n = 5 is not divisible by 4, n2 = 25 is also not divisible by 4. For n = 5, the “if” and “then” parts of the statement are both false. Therefore, n = 5 is not a counterexample to the statement. Example.
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