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Identify the steps involved in proving this statement: If mn is even, then either m is even or n is even. (Select all that apply.) We will use a direct proof. O We will use a proof by contraposition. Assume that m is odd and n is odd. Assume that m is odd or n is odd. 2s +1 and This means that there exists an integers S and t such that either m = 2s and n = 2t +1. n = 2t or such that M = U This means that there exist integers S and t such that m = 2s + 1 and = 2t + 1. %3D n = This means that (2s + 1)(2t + 1) = 4st + 2s + 2t +1 = 2(2st + s+t) +1 mn =

Identify the steps involved in proving this statement: If mn is even, then either m is even or n is even. (Select all that apply.) We will use a direct proof. O We will use a proof by contraposition. Assume that m is odd and n is odd. Assume that m is odd or n is odd. 2s +1 and This means that there exists an integers S and t such that either m = 2s and n = 2t +1. n = 2t or such that M = U This means that there exist integers S and t such that m = 2s + 1 and = 2t + 1. %3D n = This means that (2s + 1)(2t + 1) = 4st + 2s + 2t +1 = 2(2st + s+t) +1 mn =

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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Identify the steps involved in proving this statement: If mn is even, then either M is even or n is even. (Select all that apply.) We will use a direct proof. We will use a proof by contraposition. Assume that m is odd and n is odd. O Assume that m is odd or n is odd. This means that there exists an integers S and t such that either m = = 2s + 1 and n = 2t or such that m = 2s and n = 2t + 1. This means that there exist integers S and t such that m = 2s +1 and n = 2t + 1. This means that (2s + 1)(2t + 1) = 4st + 2s + 2t +1= 2(2st + s+t) +1 mn
Transcribed Image Text:Identify the steps involved in proving this statement: If mn is even, then either M is even or n is even. (Select all that apply.) We will use a direct proof. We will use a proof by contraposition. Assume that m is odd and n is odd. O Assume that m is odd or n is odd. This means that there exists an integers S and t such that either m = = 2s + 1 and n = 2t or such that m = 2s and n = 2t + 1. This means that there exist integers S and t such that m = 2s +1 and n = 2t + 1. This means that (2s + 1)(2t + 1) = 4st + 2s + 2t +1= 2(2st + s+t) +1 mn
This means that there exists an integers S and t such that either m = 2s n = 2t or such that m 2s and n = 2t + 1. UThis means that there exist integers S and t such that m = 2s +1 and n = 2t + 1. %3D U This means that (2s + 1)(2t + 1) = 4 st + 2s + 2t + 1=2(2st + mn = In either case, mn has a factor of 2 in the product. Therefore, mn is odd, which completes the proof. Therefore, mn is even, which completes the proof.
Transcribed Image Text:This means that there exists an integers S and t such that either m = 2s n = 2t or such that m 2s and n = 2t + 1. UThis means that there exist integers S and t such that m = 2s +1 and n = 2t + 1. %3D U This means that (2s + 1)(2t + 1) = 4 st + 2s + 2t + 1=2(2st + mn = In either case, mn has a factor of 2 in the product. Therefore, mn is odd, which completes the proof. Therefore, mn is even, which completes the proof.
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