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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
23. Prove part 1 of Theorem 2.
24. Let m be a fixed positive number. On the set consider the following two equivalence relations:
a. a
m
b, that is, aRb if and only if a b = mk for some integer k.
b. aSb if and only if a and b have the same remainder when divided by m.
Prove that a.) a
m
b if and only if aSb; and b.) the two equivalence relations determine the same
classes.
25. On the set define the following two equivalence relations:
a. aRb if and only if a
4
= b
4
.
b. aSb if and only if |a|=|b|.
Prove that aRb if and only if aSb. Then determine the equivalence classes.
THE BASICS OF GROUPS
As it is possible to see from the other mathem atical to ...
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Publisher Resources

ISBN: 9780123822178