In each of the cases below, determine whether the set U; is open or not, and briefly justify your answers: (i) U1 = {z € C; |z| <1 and |z– 1|<1 and |z- i| < 1} (ii) U2 = {z € C; Re z > 0} (iii) U3 = {z E C; Im z > 0}n{z € C; |z + 10i| < 2}

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A: A set of numbers is well ordered when each of its nonempty subsets has a minimum element.

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Q: (a) Let S be a set of real numbers with the property that if x1, x2 € S, then the midpoint (x1 + x2)…

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Q: If A = {2 ≤ x ≤ 5) and B = {3≤ x ≤6), find A UB, AB, and (AU B)(AB).

A: In set theory, the symbols ∪ and ∩ are used to denote the union and intersection of sets…

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Q: Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

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A: Given, f(x) := x² for x∊ R,  E := {x∊ R : -1≤x≤0} and F := {x∊ R : 0≤x≤1}.

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Q: 2 Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2. If t(x) = 5x² + x + 2 € P₂,…

A: Answer Explanation:Step 1: Step 2: Step 3: Step 4:

Q: QUESTION 1 Let F(x.y): x is friend with y". N(x): "x is funny", W(x): "x is wise". R(x): x is fair".…

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