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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.)

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter8: Complex Numbers And Polarcoordinates
Section: Chapter Questions
Problem 2RP: A Bitter Dispute With the publication of Ars Magna, a dispute intensified between Jerome Cardan and...
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Problem 1 Consider 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 want to 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, show that the converse is not true by providing an example that demonstrates it is not true.)
Transcribed Image Text:Problem 1 Consider 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 want to 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, show that the converse is not true by providing an example that demonstrates it is not true.)
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