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Select the collection of sets that forms a partitic

Select the collection of sets that forms a partitic

Advanced Engineering Mathematics
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:** Select the collection of sets that forms a partition of \( R \). **Options:** 1. - \( \{ x \in R : x < 4 \} \) - \( \{ x \in R : 2 \leq x \leq 4 \} \) - \( \{ x \in R : 2 < x \} \) 2. - \( \{ x \in R : x < 2 \} \) - \( \{ x \in R : 2 \leq x < 4 \} \) - \( \{ x \in R : 4 \leq x \} \) 3. - \( \{ x \in R : x \leq 2 \} \) - \( \{ x \in R : 2 < x < 4 \} \) - \( \{ x \in R : 4 < x \} \) 4. - \( \{ x \in R : x < 2 \} \) - \( \{ x \in R : 2 < x < 4 \} \) - \( \{ x \in R : 4 \leq x \} \) **Explanation:** Choose the correct partition from the options where each interval divides the set of real numbers \( R \) such that: - Each subset is non-empty. - The union of all subsets equals \( R \). - Subsets are pairwise disjoint.
Transcribed Image Text:**Question:** Select the collection of sets that forms a partition of \( R \). **Options:** 1. - \( \{ x \in R : x < 4 \} \) - \( \{ x \in R : 2 \leq x \leq 4 \} \) - \( \{ x \in R : 2 < x \} \) 2. - \( \{ x \in R : x < 2 \} \) - \( \{ x \in R : 2 \leq x < 4 \} \) - \( \{ x \in R : 4 \leq x \} \) 3. - \( \{ x \in R : x \leq 2 \} \) - \( \{ x \in R : 2 < x < 4 \} \) - \( \{ x \in R : 4 < x \} \) 4. - \( \{ x \in R : x < 2 \} \) - \( \{ x \in R : 2 < x < 4 \} \) - \( \{ x \in R : 4 \leq x \} \) **Explanation:** Choose the correct partition from the options where each interval divides the set of real numbers \( R \) such that: - Each subset is non-empty. - The union of all subsets equals \( R \). - Subsets are pairwise disjoint.
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