(a) Give a proof by contradiction of: for all x € R, if x² is irrational, then x is irratio (b) Give a proof by contraposition of: for all integers n, if 3n - 5 is even, then n is o (c) Give a proof by cases of: x ≤ |x| for all real numbers x. (d) Give a direct proof of: if x and y are odd integers, then x + y is even.” Lo 1 I 1 Lal 11

(a) Give a proof by contradiction of: for all x € R, if x² is irrational, then x is irratio (b) Give a proof by contraposition of: for all integers n, if 3n - 5 is even, then n is o (c) Give a proof by cases of: x ≤ |x| for all real numbers x. (d) Give a direct proof of: if x and y are odd integers, then x + y is even.” Lo 1 I 1 Lal 11

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section: Chapter Questions

Problem 15RP

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