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Mathematics, 06.05.2020 04:45 kevinleon695

5. For each of the following, prove that the relation is an equivalence relation. Then give information about the equivalence classes as specified: a) The relation β„› = {(xx, yy) ∈ ℝ Γ— ℝ: (xx βˆ’ yy) ∈ β„š } on ℝ. Describe the equivalence classes of 0; 1 2 ; √7. b) The relation = οΏ½οΏ½(xx, yy), (aa, bb)οΏ½: xx2 + yy2 = aa2 + bb2οΏ½ on ℝ Γ— ℝ . Sketch the equivalence classes of (1, 2); (4, 0). c) The relation = {(xx, yy) ∈ ℝ Γ— ℝ: sin(xx) = sin(yy)} on ℝ. Describe the equivalence classes of 0; ππ 2 ; ππ 4

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