Lecture 1.6: Proof Techniques (contd)

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Lecture 1.6: Proof Techniques (contd) CS 250, Discrete Structures, Fall 2014 Nitesh Saxena Adopted from previous lectures by Cinda Heeren

Lecture 1.6 - Proof Techniques (contd.) Course Admin HW1 Due at 11am on Sep 18 Please follow all instructions Questions? 4/14/2019 Lecture 1.6 - Proof Techniques (contd.)

Lecture 1.6 - Proof Techniques (contd.) Outline Proof Techniques (more examples) 4/14/2019 Lecture 1.6 - Proof Techniques (contd.)

Lecture 1.6 - Proof Techniques (contd.) Black Board Exercises Prove the following: If n is an integer and n2 is odd, then n is odd. If m and n are both perfect squares, then nm is also a perfect square. If n is an integer and n3 + 5 is odd, then n is even If m and n are integers, and mn is even, then m is even or n is even If n is a positive integer, then n is even if and only if 7n + 4 is even Sqrt(2) is irrational 4/14/2019 Lecture 1.6 - Proof Techniques (contd.)

Lecture 1.6 - Proof Techniques (contd.) Today’s Reading Rosen 1.7 Please solve the exercises at the end of each chapter section. They are fun. 4/14/2019 Lecture 1.6 - Proof Techniques (contd.)