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? Why or why not?Yes, because the union of the sets V1, V2, V3, ... is empty.Yes, because no two of the sets V1, V2, V3, ... have any elements in common. Yes, because the intersection of the sets V1, V2, V3, ... is empty.No, because the sets V1, V2, V3, ... are disjoint.No, because no two of the sets V1, V2, V3, ... are disjoint.(d)∪ni = 1Vi = (e)∩ni = 1Vi = (f)∪∞i = 1Vi = (g)∩∞i = 1Vi = Let Ri = x ∈ R 1 ≤ x ≤ 1 + 1i = 1, 1 + 1i for each positive integer i. (Enter your answers using interval notation.)(a)∪ 9 i = 1 Ri = (b)∩ 9 i = 1 Ri = (c)Are R1, R2, R3, , R9 mutually disjoint? Why or why not?Yes, because the union of the sets R1, R2, R3, ..., R9 is empty.Yes, because no two of the sets R1, R2, R3, ..., R9 have any elements in common. Yes, because the intersection of the sets R1, R2, R3, ..., R9 is empty.No, because the sets R1, R2, R3, ..., R9 are disjoint.No, because no two of the sets R1, R2, R3, ..., R9 are disjoint.(d)∪ n i = 1 Ri = (e)∩ n i = 1 Ri = (f)∪ ∞ i = 1 Ri = (g)∩ ∞ i = 1 Ri = Let V; =Rfor each positive integer i. Find each of the following. (Enter your answers using interval notation.)(а) 4UV, =i = 1(b)i = 1(c) Are V,, V,, V3,... mutually disjoint? Why or why not?O Yes, because the union of the sets V,, V2, V3, ...is empty.O Yes, because no two of the sets V,, V,, Varhave any elements in common....O Yes, because the intersection of the sets V,, V,, V3, ... is empty.O No, because the sets V,, V,, V3,... are disjoint.O No, because no two of the sets V,, V,, V3, ... are disjoint.1+(d) ni = 1(e)ni = 1(f)U V; =i = 1(g)=| = 1 Let R, = {x€R 15= |1, 1 +for each positive integer i. (Enter your answers using interval notation.)(a)9U R; =i = 1(b)N R; =i = 1(c) Are R,, R2, R3, ..., R, mutually disjoint? Why or why not?O Yes, because the union of the sets R,, R,, R3,R. is empty.O Yes, because no two of the sets R,, R,, R3,R, have any elements in common....O Yes, because the intersection of the sets R,, R,, R,, ..., R, is empty.O No, because the sets R,, R2, R3,R, are disjoint.O No, because no two of the sets R,, R,, R2, ..., R, are disjoint.(d)nU R;=i = 1(e)N R; =i = 1(f)R; =i = 1(g)N R; =i = 1

Answered: Image /qna-images/answer/45510b48-44d3-496e-9074-0cd608c8a5cc.jpg

Answered: Let V; = R for each positive integer i.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

100%

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 =

(c)

Are

V₁, V₂, V₃,

mutually disjoint? Why or why not?

Yes, because the union of the sets V₁, V₂, V₃, ... is empty.Yes, because no two of the sets V₁, V₂, V₃, ... have any elements in common. Yes, because the intersection of the sets V₁, V₂, V₃, ... is empty.No, because the sets V₁, V₂, V₃, ... are disjoint.No, because no two of 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 =

Let

R_i =

x ∈ R

1 ≤ x ≤ 1 +

1, 1 +

for each positive integer i. (Enter your answers using interval notation.)

(a)

∪ ⁹ _{i = 1} R_i =

(b)

∩ ⁹ _{i = 1} R_i =

(c)

Are

R₁, R₂, R₃, , R₉

mutually disjoint? Why or why not?

Yes, because the union of the sets R₁, R₂, R₃, ..., R₉ is empty.Yes, because no two of the sets R₁, R₂, R₃, ..., R₉ have any elements in common. Yes, because the intersection of the sets R₁, R₂, R₃, ..., R₉ is empty.No, because the sets R₁, R₂, R₃, ..., R₉ are disjoint.No, because no two of the sets R₁, R₂, R₃, ..., R₉ are disjoint.

(d)

∪ ⁿ _{i = 1} R_i =

(e)

∩ ⁿ _{i = 1} R_i =

(f)

∪ ^∞ _{i = 1} R_i =

(g)

∩ ^∞ _{i = 1} R_i =