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
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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 \(A_i\).

---
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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