1. (a) Each of the following true statements contains an implication. (i) For all a, b E Z, if a – b is even then a + b is even. (ii) For all A C N, if A is finite then Ac is infinite. Write down the converse of each statement and decide (with justifica- tion) whether it is true or false. (b) Consider the statement: For all r, y, z E Z. At least one of x - y, x- z and y -z is even. (i) Write down a roadmap for a proof of this statement by contradic- tion. (ii) Fill in the details of your roadmap to prove the statement.

1. (a) Each of the following true statements contains an implication. (i) For all a, b E Z, if a – b is even then a + b is even. (ii) For all A C N, if A is finite then Ac is infinite. Write down the converse of each statement and decide (with justifica- tion) whether it is true or false. (b) Consider the statement: For all r, y, z E Z. At least one of x - y, x- z and y -z is even. (i) Write down a roadmap for a proof of this statement by contradic- tion. (ii) Fill in the details of your roadmap to prove the statement.

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Description: 1.(a) Each of the following true statements contains an implication.(i) For all a, b E Z, if a – b is even then a + b is even.(ii) For all A C N, if A is finite then Aº is infinite.Write down the converse of each statement and decide (with justifica

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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