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5.1 In each case, determine whether or not H is a subgroup of G. a) G=(R, +); H=Q b) G=(Q, +); H=Z c) G=(Z, +); H=Z* d) G=(Q-(0}, ); H=Q*

5.1 In each case, determine whether or not H is a subgroup of G. a) G=(R, +); H=Q b) G=(Q, +); H=Z c) G=(Z, +); H=Z* d) G=(Q-(0}, ); H=Q*

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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5.1 In each case, determine whether or not H is a subgroup of G. a) G=(R, +); H=Q b) G=(Q, +); H=Z c) G=(Z, +); H=Z* d) G=(Q-(0}, ); H=Q+ e) G=(Zg, Ð); H=(0,2,4} f) G=the set of 2-tuples of real numbers (a,b) under addition of 2-tuples; H=the subset consisting of all 2-tuples such that b=-a g) G=Qs; H={I, J, K} h) G=(P(X), A); H={Ø, A, B, A AB}, where A, B are two elements of G i) G=(P(X), A); H=P(Y), where YCX.
Transcribed Image Text:5.1 In each case, determine whether or not H is a subgroup of G. a) G=(R, +); H=Q b) G=(Q, +); H=Z c) G=(Z, +); H=Z* d) G=(Q-(0}, ); H=Q+ e) G=(Zg, Ð); H=(0,2,4} f) G=the set of 2-tuples of real numbers (a,b) under addition of 2-tuples; H=the subset consisting of all 2-tuples such that b=-a g) G=Qs; H={I, J, K} h) G=(P(X), A); H={Ø, A, B, A AB}, where A, B are two elements of G i) G=(P(X), A); H=P(Y), where YCX.
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