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5. Figure (a) gives the addition table for Z4, the integers modulo 4 under addition; and Figure (b) gives the partial multiplication table for S = {1, 3, 7, 9) in Z10. Are (Z4, +) and (S, x) semi-groups, monoids or groups? Find out a homomorphism mapping between (Z4, +) and (S, x). + 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 3 0 1 2 (a) X 1 3 7 9 1 1 3 7 3 9 1 9 3 3 7 1 9 7 (b) 9 7 9 7 3 1

5. Figure (a) gives the addition table for Z4, the integers modulo 4 under addition; and Figure (b) gives the partial multiplication table for S = {1, 3, 7, 9) in Z10. Are (Z4, +) and (S, x) semi-groups, monoids or groups? Find out a homomorphism mapping between (Z4, +) and (S, x). + 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 3 0 1 2 (a) X 1 3 7 9 1 1 3 7 3 9 1 9 3 3 7 1 9 7 (b) 9 7 9 7 3 1

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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5. Figure (a) gives the addition table for Z4, the integers modulo 4 under addition; and Figure (b) gives the partial multiplication table for S = {1, 3, 7, 9) in Z10. Are (Z4, +) and (S, x) semi-groups, monoids or groups? Find out a homomorphism mapping between (Z4, +) and (S, x). + 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 3 0 1 2 G X 1 3 7 9 1 3 1 7 9 3 7 9 3 9 1 7 7 1 9 3 9 7 3 1 (b)
Transcribed Image Text:5. Figure (a) gives the addition table for Z4, the integers modulo 4 under addition; and Figure (b) gives the partial multiplication table for S = {1, 3, 7, 9) in Z10. Are (Z4, +) and (S, x) semi-groups, monoids or groups? Find out a homomorphism mapping between (Z4, +) and (S, x). + 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 3 0 1 2 G X 1 3 7 9 1 3 1 7 9 3 7 9 3 9 1 7 7 1 9 3 9 7 3 1 (b)
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