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Problem 2: Consider the set of integers. 1. Use a direct proof to show that the sum of two odd integers is even. 2. Use a direct proof to show that the product of two odd integers is odd.

Problem 2: Consider the set of integers. 1. Use a direct proof to show that the sum of two odd integers is even. 2. Use a direct proof to show that the product of two odd integers is odd.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Problem 2: Consider the set of integers. 1. Use a direct proof to show that the sum of two odd integers is even. 2. Use a direct proof to show that the product of two odd integers is odd. Prove that if n is an integer and n³ + 5 is odd, then n is even using a) A proof by contraposition. 3. b) A proof by contradiction. 4. Prove or disprove that if m and n are integers such that mn = 1, then either m = 1 and n = 1, or else m = -1 and n = -1. 5. Prove that these four statements about the integer n are equivalent: a) n² is odd. b) 1 - n is even. c) n³ is odd. d) n² + 1 is even. 6. Prove that if m and n are integers and mn is even, then m is even or n is even.
Transcribed Image Text:Problem 2: Consider the set of integers. 1. Use a direct proof to show that the sum of two odd integers is even. 2. Use a direct proof to show that the product of two odd integers is odd. Prove that if n is an integer and n³ + 5 is odd, then n is even using a) A proof by contraposition. 3. b) A proof by contradiction. 4. Prove or disprove that if m and n are integers such that mn = 1, then either m = 1 and n = 1, or else m = -1 and n = -1. 5. Prove that these four statements about the integer n are equivalent: a) n² is odd. b) 1 - n is even. c) n³ is odd. d) n² + 1 is even. 6. Prove that if m and n are integers and mn is even, then m is even or n is even.
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