### Understanding Set Relationships: An ExampleConsider the following sets:\[ A = \{2n : n \in \mathbb{N}\} \]\[ B = \{n \in \mathbb{Z} : n^2 \text{ is even}\} \]Determine the relationship between these two sets. Select the correct option below:1. $ \circ $ Neither set is a subset of the other.2. $ \circ $ $ A \subset B $.3. $ \circ $ $ A \subseteq B $, and $ B \subseteq A $.4. $ \circ $ $ B \subset A $.

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Answered: Let A = {2n : n e N}, and B = {n E Z :…

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Let A = {2n : n e N}, and B = {n E Z : n² is even}. Neither set is a subset of the other. O AC B. O AC B, andB A. ВСА.

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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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

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### Understanding Set Relationships: An Example

Consider the following sets:

\[ A = \{2n : n \in \mathbb{N}\} \]
\[ B = \{n \in \mathbb{Z} : n^2 \text{ is even}\} \]

Determine the relationship between these two sets. Select the correct option below:

1. $ \circ $ Neither set is a subset of the other.
2. $ \circ $ $ A \subset B $.
3. $ \circ $ $ A \subseteq B $, and $ B \subseteq A $.
4. $ \circ $ $ B \subset A $.

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