Calculate each of the following unions and intersections, and circle your final answer.i. U(-n, n) =n=1.ñ(-1-) -ii.n=1iii. N(-n, n)nƐZ

(i) Given ∪n=1∞−n,n Expand the union ∪n=1∞−n,n=−1,1∪−2,2∪−3,3∪−4,4∪...........∪−∞,∞=−∞,∞ Since,…

Answered: Calculate each of the following unions…

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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Calculate each of the following unions and intersections, and circle your final answer.
i. U(-n, n) =
n=1
.ñ(-1-) -
ii.
n=1
iii. N(-n, n)
nƐZ

Expert Solution

Step 1

(i) Given $\cup_{n = 1}^{\infty} (- n, n)$

Expand the union

$\begin{matrix} \cup_{n = 1}^{\infty} (- n, n) = (- 1, 1) \cup (- 2, 2) \cup (- 3, 3) \cup (- 4, 4) \cup ........... \cup (- \infty, \infty) \\ = (- \infty, \infty) (Since, (- n, n) \subseteq (- n + 1, n + 1)) \\ = R (Set of real number) \end{matrix}$

Therefore, $\cup_{n = 1}^{\infty} (- n, n) = (- \infty, \infty) = R$

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