Homework 2 Methods of Proof Solutions d Proof Note 500 2 250 000 and 501 2 251

Homework 2 methods of proof solutions d proof note

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Problem 2.5 (Proofs by Cases).(a) Prove the for any integern, then number3n2+n+ 14is even.(b) Prove that for every real numberx, we havex+|x-7| ≥7. Problem 2.6 (Proofs by Contraposition).(a) Give a contrapositive proof of the following: For any integern, if11n-5is odd, thennis even.(b) Give a contrapositive proof of the following: For any integern, if5-n2, then5-n. Recalla-bmeansadoes not divideb.(c)(i) Prove that ifn2-1is even, thennis odd.(ii) Using part (i) prove that ifn2-1is even, thenn2-1is divisible by4. Solution 2.6.
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Homework 2: Methods of Proof Solutions
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