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Unformatted text preview: Math 210 Homework 5
Due Monday March 14th
1. Let R be the relation on Z deﬁned by
(x, y ) ∈ R if and only if y − x ≥ 10. (i) Is R reﬂexive?
(ii) Is R symmetric?
(iii) Is R transitive?
(iv) Is R an equivalence relation?
(v) Is R a partial order?
2. Find q and r as deﬁned in the Division Algorithm in each of these cases.
(i) a = 163, b = 7
(ii) a = 163, b = −7
(iii) a = −163, b = 7
(iv) a = −163, b = −7
3. Prove that if n is an integer, then either n2 or n2 − 1 is divisible by 3.
4. Let A = {1, 2, 4, 8, 16, 32, 64, 128}. Show that the relation “x divides y ”
is a total order on A. 1 ...
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This note was uploaded on 12/07/2011 for the course MATH 210 taught by Professor Staff during the Spring '08 term at University of Delaware.
 Spring '08
 Staff
 Math

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