601Problem 2.1: Which of the following are groups? Why?(a) R under addition(b) The set 3Z of integers that are multiples of 3, under addition.(c) R (0) under the operation ab= lab).(d) The sel {1,-1) under multiplication(e) The subset of Q consisting of all rational numbers with rational square roots, under multiplication.(f) The set of all pairs (z,y) of real numbers, under the operation (x,y) (z, w) = (x+z₁y-w).(g) The set of all pairs (z,y) of real numbers with y 0, under the operation (z,y) (2, w) = (x+z, yw).(h) R {1}), under the operation a+b=a+b-ab.(i) Z, under the operation ab=a+b=1.

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Answered: Problem 2.1: Which of the following are…

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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Problem 2.1: Which of the following are groups? Why? (a) R under addition (b) The set 3Z of integers that are multiples of 3, under addition. (c) R (0) under the operation ab=labl.