Determine whether the binary operation gives a group structure on the given set. If no group results, identify the group property that does not hold. a) Let be defined on 2Z = {2n/n € Z) by a + b = a - b. b) Let be defined on Q by a = b = ab. c) Letbe defined on R by a + b = |ab| d) Letbe defined on Z by a b = ab +a+1

Determine whether the binary operation gives a group structure on the given set. If no group results, identify the group property that does not hold. a) Let be defined on 2Z = {2n/n € Z) by a + b = a - b. b) Let be defined on Q by a = b = ab. c) Letbe defined on R by a + b = |ab| d) Letbe defined on Z by a b = ab +a+1

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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Question

B. Determine whether the binary operation • gives a group structure on the given set.
If no group results, identify the group property that does not hold.
a) Let + be defined on 2Z = {2n/n E Z} by a + b = a – b.
b) Let + be defined on Q by a • b = ab.
c) Let + be defined on R by a + b = |ab|
d) Let + be defined on Z by a + b = ab + a +1

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Step 2: Identifying the nature of first binary operation

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Step 3: Identifying the nature of second binary operation

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Step 4: Identifying the nature of third binary operation

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Step 5: Identifying the nature of fourth binary operation

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