(11) Let Z, denotes the integers (mod n), e.g., Z,, denotes the 10 equivalence classes Z1, = {[0], [1], [2], [3], [4], [5],[6],[7],[8],[9]} . ) Define f:Z21→Z,, × Z, as follows. For [x]€Z21, define '17 f([x]) = (x (mod 13), x (mod 17)). (a) f is 1-1, True or False? (circle one) Why? (b) f is onto, True or False? (circle one) Why? (c) f has an inverse, True or False? (circle one) Why?
(11) Let Z, denotes the integers (mod n), e.g., Z,, denotes the 10 equivalence classes Z1, = {[0], [1], [2], [3], [4], [5],[6],[7],[8],[9]} . ) Define f:Z21→Z,, × Z, as follows. For [x]€Z21, define '17 f([x]) = (x (mod 13), x (mod 17)). (a) f is 1-1, True or False? (circle one) Why? (b) f is onto, True or False? (circle one) Why? (c) f has an inverse, True or False? (circle one) Why?
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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![(11) Let Z, denotes the integers (mod n), e.g., Z,, denotes the 10
equivalence classes Z, = ([0],[1],[2],[3],[4],[5],[6],[7],[8],[9]} . )
Define f:Z,21→Z, × Z,, as follows. For [x]€Z»„, define
f([x]) = (x (mod 13), x (mod 17)).
(a) f is 1-1, True or False? (circle one) Why?
(b) f is onto, True or False? (circle one) Why?
(c) f has an inverse, True or False? (circle one) Why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34a6820a-e392-4bc6-a071-8d3939523d24%2F977a3b59-a69b-4e46-b4c6-034cfd87a5b5%2Fiwzgry_processed.png&w=3840&q=75)
Transcribed Image Text:(11) Let Z, denotes the integers (mod n), e.g., Z,, denotes the 10
equivalence classes Z, = ([0],[1],[2],[3],[4],[5],[6],[7],[8],[9]} . )
Define f:Z,21→Z, × Z,, as follows. For [x]€Z»„, define
f([x]) = (x (mod 13), x (mod 17)).
(a) f is 1-1, True or False? (circle one) Why?
(b) f is onto, True or False? (circle one) Why?
(c) f has an inverse, True or False? (circle one) Why?
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