This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECS20 Handout 9 January 27, 2011 Proof Techniques I 1. Direct proof . The implication p q can be proved by showing that if p is true, then q must also be true. A proof of this kind is called a direct proof . Example: Prove that If n is odd, then n 2 is odd 2. Indirect proof . Since the implication p q is equivalent to its contrapositive q p , the implication p q can be proved by showing that its contrapositive q p is true. This related implication is usually proved directly. An argument of this type is called an indirect proof . Example: Prove that if 3 n + 2 is odd, then n is odd. 3. Proof by contradiction . By assuming that the hypothesis p is true, and that the conclusion q is fals, then using p and q as well as other axioms, definitions, and previously derived theorems, derives a contradiction. Proof by contradiction can be justified by noting that ( p q ) ( p q r r ) Examples: (a) Prove that 2 is irrational (b) Prove that: For all real numbers...
View
Full
Document
This note was uploaded on 05/31/2011 for the course ECS 20 taught by Professor Staff during the Winter '08 term at UC Davis.
 Winter '08
 Staff

Click to edit the document details