Determine whether each of the following is a function: (a) f : Z12 → Z6 by f([x]12) = [æ]6. (b) f : Z12 → Z5 by f([x]12) = [x]5. (c) f : Z12 → Zs by f([x]12) = [2x]s.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Determine whether each of the following is a function:

(a) \( f : \mathbb{Z}_{12} \to \mathbb{Z}_6 \) by \( f([x]_{12}) = [x]_6 \).

(b) \( f : \mathbb{Z}_{12} \to \mathbb{Z}_5 \) by \( f([x]_{12}) = [x]_5 \).

(c) \( f : \mathbb{Z}_{12} \to \mathbb{Z}_8 \) by \( f([x]_{12}) = [2x]_8 \).
Transcribed Image Text:Determine whether each of the following is a function: (a) \( f : \mathbb{Z}_{12} \to \mathbb{Z}_6 \) by \( f([x]_{12}) = [x]_6 \). (b) \( f : \mathbb{Z}_{12} \to \mathbb{Z}_5 \) by \( f([x]_{12}) = [x]_5 \). (c) \( f : \mathbb{Z}_{12} \to \mathbb{Z}_8 \) by \( f([x]_{12}) = [2x]_8 \).
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