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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
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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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.
Transcribed Image Text: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.
Expert Solution
Step 1

(a)   f:ℤ→ℤ12

 f(1)   =812   =8f(2)   =1612 =4f(3)   =2412 =0f(4)   =3212 =8f(-1)=-812=4

∴ S=ℤ ⇒ f(S)=0, 4, 8

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