210hw5 - Math 210 Homework 5 Due Monday March 14th 1. Let R...

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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.

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