if f : S →T is a function, then there is a bijection between f(S) and defined by a ~f b if f(a) = f(b). For each of the following functions find f(S) and S/f and exhibit the bijection between them the equivalence classes of S/f for the equivalence relation (a) f : Z → Z12 given by f(n) = [8n]12. (b) f : Z12 → Z12 given by f(a]12) = [5x]12- (c) f : Z24 → Z24 given by f([x]24) = [4x]24.

if f : S →T is a function, then there is a bijection between f(S) and defined by a ~f b if f(a) = f(b). For each of the following functions find f(S) and S/f and exhibit the bijection between them the equivalence classes of S/f for the equivalence relation (a) f : Z → Z12 given by f(n) = [8n]12. (b) f : Z12 → Z12 given by f(a]12) = [5x]12- (c) f : Z24 → Z24 given by f([x]24) = [4x]24.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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