1. CSE 20 – Discrete Mathematics Dr. Cynthia Bailey Lee Dr. Shachar Lovett Peer Instruction in Discrete Mathematics by Cynthia Leeis licensed under a Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License. Based on a work at http://peerinstruction4cs.org. Permissions beyond the scope of this license may be available at http://peerinstruction4cs.org.Cynthia LeeCreative Commons Attribution- NonCommercial-ShareAlike 4.0 International Licensehttp://peerinstruction4cs.org

2. Today’s Topics: 1. More review of Proof by Contradiction  Irrational numbers 2

3. 1. Proof by Contradiction Following up on a very common source of errors on the previous midterm. 3

4. Proof by Contradiction Steps  What are they? A. 1. Assume what you are proving, 2. plug in definitions, 3. do some work, 4. show the opposite of what you are proving (a contradiction). B. 1. Assume the opposite of what you are proving, 2. plug in definitions, 3. do some work, 4. show the opposite of your assumption (a contradiction). C. 1. Assume the opposite of what you are proving, 2. plug in definitions, 3. do some work, 4. show the opposite of some fact you already showed (a contradiction). D. Other/none/more than one. 4

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7. 7 Is there a shorter way that reaches a contradiction sooner?

8. 8 Is this proof valid? A.YES B.NO