Search results with tag "Direct proof"
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
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.
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!