Chapter 6.1, Problem 23ES

Let $V_i=\left\{x\in R|-\frac{1}{i}\le x\le \frac{1}{i}\right\}=\left[-\frac{1}{i},\frac{1}{i}\right]$ for each positive integer i.

a. ${\displaystyle \underset{i=0}{\overset{4}{\cup }}{V}_i=?}$

b. ${\displaystyle \underset{i=0}{\overset{4}{\cap }}{V}_i=?}$

c. Are mutually disjoint $V_1{V}_2{V}_3,\mathrm{...}$ mutually disjoint? Explain.

d. ${\displaystyle \underset{i=0}{\overset{n}{\cup }}{V}_i=?}$

e. ${\displaystyle \underset{i=0}{\overset{n}{\cap }}{V}_i=?}$

f. ${\displaystyle \underset{i=0}{\overset{\infty }{\cup }}{V}_i=?}$

g. ${\displaystyle \underset{i=0}{\overset{\infty }{\cap }}{V}_i=?}$