Let A = {-i, .,-2, –1,0,1, 2, . i}. Compute the following a) U는1Ai A? = {?} A? = {?}
Let A = {-i, .,-2, –1,0,1, 2, . i}. Compute the following a) U는1Ai A? = {?} A? = {?}
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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**Mathematical Set Operations**
Given the set \(A_i = \{-i, \ldots, -2, -1, 0, 1, 2, \ldots, i\}\). Compute the following:
a) \[
\bigcup_{i=1}^{n} A_i
\]
Determine the set \(A_?\).
b) \[
\bigcap_{i=1}^{n} A_i
\]
Determine the set \(A_?\).
### Explanation:
#### Part (a): Union of Sets
The union of sets \(A_i\) from \(i=1\) to \(n\) combines all unique elements from each set \(A_i\).
#### Part (b): Intersection of Sets
The intersection of sets \(A_i\) from \(i=1\) to \(n\) includes only elements that are present in every set \(A_i\).
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Transcribed Image Text:---
**Mathematical Set Operations**
Given the set \(A_i = \{-i, \ldots, -2, -1, 0, 1, 2, \ldots, i\}\). Compute the following:
a) \[
\bigcup_{i=1}^{n} A_i
\]
Determine the set \(A_?\).
b) \[
\bigcap_{i=1}^{n} A_i
\]
Determine the set \(A_?\).
### Explanation:
#### Part (a): Union of Sets
The union of sets \(A_i\) from \(i=1\) to \(n\) combines all unique elements from each set \(A_i\).
#### Part (b): Intersection of Sets
The intersection of sets \(A_i\) from \(i=1\) to \(n\) includes only elements that are present in every set \(A_i\).
---
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