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.

Name: 1.(a) Each of the following true statements contains an implication.(
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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

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.CT: Test

Problem 3CT: To prove a theorem of the form "If P, then Q" by the indirect method, the first line of the proof...

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