if f : S →T is a function, then there is a bijection between f(S) and 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 defined by a ~f (a) f : Z → Z12 given by f(n) = [8n]12. (b) f : Z12 → Z12 given by f([x]12) = [5x]12- (c) f : Z24 → Z24 given by f([x]24) = [4x]24. (d) f : Z24 → Z12 given by f([a]24) = [4x]12-
if f : S →T is a function, then there is a bijection between f(S) and 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 defined by a ~f (a) f : Z → Z12 given by f(n) = [8n]12. (b) f : Z12 → Z12 given by f([x]12) = [5x]12- (c) f : Z24 → Z24 given by f([x]24) = [4x]24. (d) f : Z24 → Z12 given by f([a]24) = [4x]12-
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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please just answer (d)
![if f : S →T is a function, then there is a bijection between f(S) and
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
defined by a ~f
(a) f : Z → Z12 given by f(n) = [8n]12.
(b) f : Z12 → Z12 given by f([x]12) = [5x]12-
(c) f : Z24 → Z24 given by f([x]24) = [4x]24.
(d) f : Z24 → Z12 given by f([a]24) = [4x]12-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c6dc250-aacb-41a7-9d0f-af7925cc550a%2Fedc0e3a5-9ed7-439f-966c-77e8cec5f40f%2Fy4cac1p_processed.png&w=3840&q=75)
Transcribed Image Text:if f : S →T is a function, then there is a bijection between f(S) and
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
defined by a ~f
(a) f : Z → Z12 given by f(n) = [8n]12.
(b) f : Z12 → Z12 given by f([x]12) = [5x]12-
(c) f : Z24 → Z24 given by f([x]24) = [4x]24.
(d) f : Z24 → Z12 given by f([a]24) = [4x]12-
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