A relation R on R² is defined by ((x1, y1), (2, 2)) R if Prove that R is an equivalence relation. (b) Let d3=1 Determine the equivalence class [(0, d3 + 1)], and illustrate it with a sketch. (c) Find all other equivalence classes, and explain why the ones you give are all the equivalence classes. x² − Y₁ = x² — Y2.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A relation R on R2 is defined by
((x1, Y₁), (x2, Y2)) = R
if
(a) Prove that R is an equivalence relation.
(b) Let d3=1
Determine the equivalence class
[(0, d3 + 1)], and illustrate it with a sketch.
(c) Find all other equivalence classes, and explain why the ones you give are all the
equivalence classes.
x² — Y₁ = x² — Y2.
Transcribed Image Text:A relation R on R2 is defined by ((x1, Y₁), (x2, Y2)) = R if (a) Prove that R is an equivalence relation. (b) Let d3=1 Determine the equivalence class [(0, d3 + 1)], and illustrate it with a sketch. (c) Find all other equivalence classes, and explain why the ones you give are all the equivalence classes. x² — Y₁ = x² — Y2.
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