In problems 4, 5: show that the relation described is (1) reflexive, (2) symmetric, (3) transitive; it is therefore an equivalence relation; (4) sketch it, by drawing the underlying set as a subset of the plane, then colouring each equivalence class in a different colour. 4. The relation ~ on Z² defined by, (a, b) ~ (c, d) if there exist m, n E N such that mb(b? –3a²) = nd(d? – 3c²).
In problems 4, 5: show that the relation described is (1) reflexive, (2) symmetric, (3) transitive; it is therefore an equivalence relation; (4) sketch it, by drawing the underlying set as a subset of the plane, then colouring each equivalence class in a different colour. 4. The relation ~ on Z² defined by, (a, b) ~ (c, d) if there exist m, n E N such that mb(b? –3a²) = nd(d? – 3c²).
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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Transcribed Image Text:In problems 4, 5: show that the relation described is (1) reflexive, (2) symmetric, (3) transitive; it is therefore an equivalence relation. (4) Sketch it by drawing the underlying set as a subset of the plane, then coloring each equivalence class in a different color.
4. The relation ∼ on \( \mathbb{Z}^2 \) defined by, \((a, b) \sim (c, d)\) if there exist \(m, n \in \mathbb{N}\) such that \(mb(b^2 - 3a^2) = nd(d^2 - 3c^2)\).
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