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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
The operation is associative. So we can group the elements in a different order to obtain
a
1
1
ða a
1
2
Þ= a
1
2
ða a
1
2
Þ:
We can use equality 4 to rewrite this last equality as
a
1
1
e = a
1
2
e:
Therefore, a
1
1
= a
1
2
. This proves that a has only one inver se elem ent.
3. Let a an d b be elements of G. The operation we are using is a binary operation on G,soa b is an
element of G. Therefore, a b has a unique inverse (see part b above). Call it x.Theinverseofthe
element a b is the element such that
ða bÞ x = x ða bÞ= e:
Lets use one of these equations to find the element x, and the o ther equation to check that the ele-
ment we found
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Publisher Resources

ISBN: 9780123822178