Answer it Problem 1Consider the following claim:Claim. {21n: n € Z} U {14n: ne Z} c{7n: ne Z}.(a) () Write the claim as an (equivalent) if-then statement.(b) (. Give a direct proof by cases that the claim is true. As a hint, you might wantto prove the if-then statement you constructed in (a).(c) (' .) State (but do not prove) the contrapositive of your statement from part (a).(d) (..) State (but do not prove) the converse of your statement from part (a).(e) (... Give a disproof by counter-example of the converse from part (d). (That is, showthat the converse is not true by providing an example that demonstrates it is not true.)

Answered: Image /qna-images/answer/6d9a72f2-f1f7-4732-9ae5-344bfc42ddd9.jpg

Laim. {21n: ne Z} U (14n: ne Z} C {7n: ne Z}. a) ( -) Write the claim as an (equivalent) if-then statement. (., Give a direct proof by cases that the claim is true. As a hint, you might want to prove the if-then statement you constructed in (a). D( .) State (but do not prove) the contrapositive of your statement from part (a). (..) State (but do not prove) the converse of your statement from part (a). (, Give a disproof by counter-example of the converse from part (d). (That is, show that the converse is not true by providing an example that demonstrates it is not true.)

Laim. {21n: ne Z} U (14n: ne Z} C {7n: ne Z}. a) ( -) Write the claim as an (equivalent) if-then statement. (., Give a direct proof by cases that the claim is true. As a hint, you might want to prove the if-then statement you constructed in (a). D( .) State (but do not prove) the contrapositive of your statement from part (a). (..) State (but do not prove) the converse of your statement from part (a). (, Give a disproof by counter-example of the converse from part (d). (That is, show that the converse is not true by providing an example that demonstrates it is not true.)

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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