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54. Let A = {..., -2, -1, 0, 1, ..., i}. Find b) A | A a) UA₁. =

54. Let A = {..., -2, -1, 0, 1, ..., i}. Find b) A | A a) UA₁. =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 69E
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**Problem 54:** Let \( A_i = \{ \ldots, -2, -1, 0, 1, \ldots, i \} \). Find: a) \( \bigcup_{i=1}^{n} A_i \). b) \( \bigcap_{i=1}^{n} A_i \). **Explanation:** This problem involves set theory and asks to find two different results related to the sets \( A_i \): 1. **Union of Sets (\(\bigcup_{i=1}^{n} A_i\))**: - The union of sets combines all elements from each set \( A_i \) for \( i = 1 \) to \( n \). This means we gather all distinct elements that appear in any of the sets. 2. **Intersection of Sets (\(\bigcap_{i=1}^{n} A_i\))**: - The intersection of sets includes only those elements that are present in every set \( A_i \) for \( i = 1 \) to \( n \). Essentially, it finds the common elements shared among all sets. These operations are fundamental concepts in set theory, often used in mathematical problem-solving and analysis.
Transcribed Image Text:**Problem 54:** Let \( A_i = \{ \ldots, -2, -1, 0, 1, \ldots, i \} \). Find: a) \( \bigcup_{i=1}^{n} A_i \). b) \( \bigcap_{i=1}^{n} A_i \). **Explanation:** This problem involves set theory and asks to find two different results related to the sets \( A_i \): 1. **Union of Sets (\(\bigcup_{i=1}^{n} A_i\))**: - The union of sets combines all elements from each set \( A_i \) for \( i = 1 \) to \( n \). This means we gather all distinct elements that appear in any of the sets. 2. **Intersection of Sets (\(\bigcap_{i=1}^{n} A_i\))**: - The intersection of sets includes only those elements that are present in every set \( A_i \) for \( i = 1 \) to \( n \). Essentially, it finds the common elements shared among all sets. These operations are fundamental concepts in set theory, often used in mathematical problem-solving and analysis.
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