Q1. Decide which of the following sets with given binary operations are groups? (i). Q* = { € QI > 0}, with a b = a+b. (ii). 22 = (0, +2, +4, +6, ...), with a b=a+b. (ii). N = {0, 1,2, 3,...}, with a b= a +b. %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Q1. Decide which of the following sets with given binary operations are
groups?
(1). Qt ( e QI> 0}, with a b a+ b.
(ii). 22 = (0, +2, +4, +6,...), with a » b =a+b.
(iii). N= (0, 1,2, 3,..., with a b a +b.
(iv). R R-(0}) with a b .
(V). (5Z, +), where 5Z = (0, +5, t10, t15, . .)
%3D
(vi) (Q") with a •b =
Transcribed Image Text:Q1. Decide which of the following sets with given binary operations are groups? (1). Qt ( e QI> 0}, with a b a+ b. (ii). 22 = (0, +2, +4, +6,...), with a » b =a+b. (iii). N= (0, 1,2, 3,..., with a b a +b. (iv). R R-(0}) with a b . (V). (5Z, +), where 5Z = (0, +5, t10, t15, . .) %3D (vi) (Q") with a •b =
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