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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
Is S transitive? If aSb and bSc,thena b 0andb c 0. By adding these two inequalities we
obtain ða bÞ+ ðb c Þ 0. Since a c 0, we can conclude that aSc. So the relation is transitive.
Is S antisymmetric? If aSb and bSa,thena b 0andb a 0. These two inequalities can be true
at the same time only if a b = 0. Thus, a = b. The fact that S is antisymmetric, reflexive, and transi-
tive implies that S is an order relation.
8. The relation T is not reflexive since a a 0. Thus it is not an equivalence relation and it is not an
order relation. The relation T is transitive.
9. The relation R is not reflexive because a a = 0 and
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Publisher Resources

ISBN: 9780123822178