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On R, with r~yifx-yeZ ) On Zx (Z - {0}), with (a, b)~ (c,d) if ad = bc. (We will need this later in the course.)

On R, with r~yifx-yeZ ) On Zx (Z - {0}), with (a, b)~ (c,d) if ad = bc. (We will need this later in the course.)

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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2. Prove that the following relations are equivalence relations: (i) On R, with x~yifx-yEZ (ii) On Zx (Z - {0}), with (a, b)~ (c,d) if ad = bc. (We will need this later in the course.)
Transcribed Image Text:2. Prove that the following relations are equivalence relations: (i) On R, with x~yifx-yEZ (ii) On Zx (Z - {0}), with (a, b)~ (c,d) if ad = bc. (We will need this later in the course.)
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