. Define the relation (x, y) ~ (x2, y2) in R if x + y =...

 

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. Define the relation (x₁, y₁) ~ (x2, y2) in R² if x² + y² = x² + y2. Show that this is an equivalence relation. Then describe the equivalence classes. . Define a relation on R² \ {(0,0)} by letting (x₁,₁) ~ (x2, y2) if there exists a nonzero such that (x1, y1) = (2x2, Ay2). Prove that defines an equivalence relation on R² \ {(0,0)}. What are the equivalence classes ? ~ . Define the relation (x₁, y₁) ~ (x2, y2) in R² if x² + y² = x² + y2. Show that this is an equivalence relation. Then describe the equivalence classes. . Define a relation on R² \ {(0,0)} by letting (x₁,₁) ~ (x2, y2) if there exists a nonzero such that (x1, y1) = (2x2, Ay2). Prove that defines an equivalence relation on R² \ {(0,0)}. What are the equivalence classes ? ~

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let X 1 X2 1 R 2 00 suppose that x 4 x2 1 So there exists ... View the full answer