Answer detailly 9(i), (ii) 9. (i) Prove by mathematical induction that for n E N,4r2 -12n +1(ii) A relation R, is defined on Z, the set of integers by aRb a - b is even.Show that R is transitive.

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Answered: 9. (i) Prove by mathematical induction…

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9. (i) Prove by mathematical induction that for n e N, Ar? – 1 2n + 1 (ii) A relation R, is defined on Z, the set of integers by aRb + a - b is even. Show that R is transitive.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 31E: 31. Prove statement of Theorem : for all integers and .

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Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.