1. Let S be the subset of Q given by S = Here, Q is the set of all rational numbers. (a) Show that the following binary operation * on S is well defined: a * b = a +b+ 5ab (a, b e S) (b) Prove that the binary structure (S, *) is a group.

1. Let S be the subset of Q given by S = Here, Q is the set of all rational numbers. (a) Show that the following binary operation * on S is well defined: a * b = a +b+ 5ab (a, b e S) (b) Prove that the binary structure (S, *) is a group.

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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1. Let S be the subset of Q given by
s - {aeQla+ }
Here, Q is the set of all rational numbers.
(a) Show that the following binary operation * on S is well defined :
а *b%3 а+b+ 5ab (а, b E S)
(b)
Prove that the binary structure (S, *) is a group.

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