100%(1)1 out of 1 people found this document helpful
This preview shows page 3 - 5 out of 5 pages.
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.