Let Vi = x ℝ − 1i ≤ x ≤ 1i = − 1i, 1i for each positive integer i. Find each of the following. (Enter your answers using interval notation.) (a)∪4i = 1Vi = (b)∩4i = 1Vi = (c) Are V1, V2, V3, mutually disjoint? Explain.a.) Yes, because the intersection of the sets V1, V2, V3, ... is empty.b.) Yes, because no two of the sets V1, V2, V3, ... have any elements in common. c.) Yes, because the union of the sets V1, V2, V3, ... is empty.d.) No, because no two of the sets V1, V2, V3, ... are disjoint.e.) No, because the sets V1, V2, V3, ... are disjoint. (d)∪ni = 1Vi = (e)∩ni = 1Vi = (f)∪∞i = 1Vi = (g)∩∞i = 1Vi =

Name: Let Vi = x ℝ − 1i ≤ x ≤ 1i = − 1i, 1i for each positive integer
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Description: Let Vi = x ℝ − 1i ≤ x ≤ 1i = − 1i, 1i for each positive integer i. Find each of the following. (Enter your answers using interval notation.) (a)∪4i = 1Vi = (b)∩4i = 1Vi = (c) Are V1, V2, V3, mutually disjoint? Explain.a.) Yes, because the in

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Answered: Let Vi = x ℝ −…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 23E

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Let

V_i =

x ℝ

−

≤ x ≤

−

for each positive integer i. Find each of the following. (Enter your answers using interval notation.)

(a)

∪⁴_{i = 1}V_i =

(b)

∩⁴_{i = 1}V_i =

a.) Yes, because the intersection of the sets V₁, V₂, V₃, ... is empty.

b.) Yes, because no two of the sets V₁, V₂, V₃, ... have any elements in common.

c.) Yes, because the union of the sets V₁, V₂, V₃, ... is empty.

d.) No, because no two of the sets V₁, V₂, V₃, ... are disjoint.

e.) No, because the sets V₁, V₂, V₃, ... are disjoint.

(d)

∪ⁿ_{i = 1}V_i =

(e)

∩ⁿ_{i = 1}V_i =

(f)

∪^∞_{i = 1}V_i =

(g)

∩^∞_{i = 1}V_i =

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