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1) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x', y') ifx

1) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x', y') ifx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x',y') ifx<x'. Is <1 a preorder? A partial order? A total order? As always, justify your answer. (b) Repeat the preceding question for the relation defined by (x, y) <2 (x',y') if x <x' and y<y. (c) Repeat the preceding question for the relation defined by (x, y) <3 (x' ,y') if x < x' or y <y'. (d) Repeat the preceding question for the relation defined by (x, y) <4 (x', y') if x < x', or x=x' and y < y. (For example, (3,4) <4 (3,5), and (4,5) <4 (5,3).)
Transcribed Image Text:(a) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x',y') ifx<x'. Is <1 a preorder? A partial order? A total order? As always, justify your answer. (b) Repeat the preceding question for the relation defined by (x, y) <2 (x',y') if x <x' and y<y. (c) Repeat the preceding question for the relation defined by (x, y) <3 (x' ,y') if x < x' or y <y'. (d) Repeat the preceding question for the relation defined by (x, y) <4 (x', y') if x < x', or x=x' and y < y. (For example, (3,4) <4 (3,5), and (4,5) <4 (5,3).)
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