18. Let V, = {* €R | 1 1 1 for each positive integer i. i 4 a. UV; = ? i=1 4 b. nV; = ? i=1 c. Are V1, V2, V3, ... mutually disjoint? Explain. d. Ü V; = ? i=1 e. n V; = ? i=1 f. ÜV; = ? %3D i=1
18. Let V, = {* €R | 1 1 1 for each positive integer i. i 4 a. UV; = ? i=1 4 b. nV; = ? i=1 c. Are V1, V2, V3, ... mutually disjoint? Explain. d. Ü V; = ? i=1 e. n V; = ? i=1 f. ÜV; = ? %3D i=1
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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![**Question 18**
Let \( V_i = \left\{ x \in \mathbb{R} \mid -\frac{1}{i} \leq x \leq \frac{1}{i} \right\} = \left[ -\frac{1}{i}, \frac{1}{i} \right] \) for each positive integer \( i \).
a. \( \bigcup_{i=1}^{4} V_i = ? \)
b. \( \bigcap_{i=1}^{4} V_i = ? \)
c. Are \( V_1, V_2, V_3, \ldots \) mutually disjoint? Explain.
d. \( \bigcup_{i=1}^{n} V_i = ? \)
e. \( \bigcap_{i=1}^{n} V_i = ? \)
f. \( \bigcup_{i=1}^{\infty} V_i = ? \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb64c1c6f-d4d7-4d8b-8ebe-5eadb49feddc%2F30daa678-4275-41c3-89c0-72d323f9d7e3%2F1bsree_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 18**
Let \( V_i = \left\{ x \in \mathbb{R} \mid -\frac{1}{i} \leq x \leq \frac{1}{i} \right\} = \left[ -\frac{1}{i}, \frac{1}{i} \right] \) for each positive integer \( i \).
a. \( \bigcup_{i=1}^{4} V_i = ? \)
b. \( \bigcap_{i=1}^{4} V_i = ? \)
c. Are \( V_1, V_2, V_3, \ldots \) mutually disjoint? Explain.
d. \( \bigcup_{i=1}^{n} V_i = ? \)
e. \( \bigcap_{i=1}^{n} V_i = ? \)
f. \( \bigcup_{i=1}^{\infty} V_i = ? \)
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