1. For each of the following, is it an equivalence relation? Prove or provide a counterexample. (a) R² \ {(0,0)}, (a, b) ~ (c, d) if there exists k € R with k ‡ 0 such that (a, b) = (kc, kd). (b) R2, (a, b)~ (c,d) if a² + b² ≥ c² +d².

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Q: 4. For (1, yı) and (r2,y2) in R² we set (11. yı) ~ (12. Y2) →{+ =3+ yi. (a) Show that ~ defines an…

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Q: 2. For universe S = R² define relation as: (a, b) ≤ (c,d) ⇒ 2a-b≤2c-d. For each of the properties…

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