Mathematics Homework Solutions
#11366
Equivalence Relations
Verify that each of the following are equivalence relations on the plane R^2 (where R are real numbers) and describe the equivalence classes geometrically.
1) (x1,y1)R(x2,y2) if and only if x1 = x2
2) (x1,y1)R(x2,y2) if and only if x1 + y1 = x2+y2
3) (x1,y1)R(x2,y2) if and only if
x1^2 + y1^2 = x2^2 + y2^2
Equivalence realtions are verified and the equivalence class is described geometrically.
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