Search results with tag "Proof by contradiction"
Direct proof
people.cs.pitt.eduProof by contradiction Direct proof In a direct proof , we prove p →q by showing that if p is true , then q must necessarily be true Example: Prove that if n is an odd integer, then n 2 is an odd integer. Proof: Assume that n is odd. That is n = (2k + 1) for some integer k.
Solutions to Homework Set 3 (Solutions to Homework ...
math.okstate.eduProof.) Suppose a 6= [0], b 6= [0] and that ab = [0]. We aim to show that ax = [1] has no solution. We will use a proof by contradiction. Suppose c is a solution of ax = [1]. Then b = b1 = b(ac) = (ab)c = [0] c = 0 : But this contradicts our original hypothesis that b is a nonzero solution of ax = [0]. Hence, there can be no solution of ax = [1].
Proof by Contradiction - Gordon College
www.math-cs.gordon.eduProof by Contradiction This is an example of proof by contradiction. To prove a statement P is true, we begin by assuming P false and show that this leads to a contradiction; something that always false. Many of the statements we prove have the form P )Q which, when negated, has the form P )˘Q. Often proof by contradiction has the form ...
Proof Techniques - Stanford University Computer Science
cs.stanford.eduIn proof by contradiction, you assume your statement is not true, and then derive a con-tradiction. This is really a special case of proof by contrapositive (where your \if" is all of mathematics, and your \then" is the statement you are trying to prove). 2. 1.2 Proof by induction 1 PROOF TECHNIQUES