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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
Exercises
11. On the set consider the relation defined as xRy if and only if x y is an integer. Prove first that R
is an equivalence relation. Then find the equivalence classes of 1, 1.32, and π.
12. On the set A = {2, 3, 4, 5, 6,} consider the rel ation defined as xRy if and only if GCD(x, y) > 1.
Is this an equivalence relation (explain how you reach your conclusion)? If it is, find [2], [3], and [8]
otherwise find some elements that are in relati on with 2, some in relation w ith 3, and some in rela-
tion with 8.
13. On the set A = {2, 3, 4, 5, 6,} consider the relation defined as xSy if and only if x and y have the
same prime factors. ...
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Publisher Resources

ISBN: 9780123822178