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
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Chapter2: Second-order Linear Odes
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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
Transcribed Image Text: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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