asubset of C

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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### Homework Question
**5.) True or False? If True, give an example. If False, give a counter-example.**

a) If A is a subset of C and B is a subset of D, then A + B is a subset of C + D.

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### Explanation
This question involves understanding the concept of subsets and set operations. You are required to analyze the given statement and determine whether it is true or false. If the statement is true, provide an example that supports the statement. If it is false, construct a counter-example to demonstrate where the statement does not hold.

Key concepts to consider:
- **Subset**: A set A is a subset of set B if every element of A is also an element of B.
- **Set Addition**: Generally involves the union of two sets.

This problem encourages logical reasoning and the application of set theory principles.
Transcribed Image Text:### Homework Question **5.) True or False? If True, give an example. If False, give a counter-example.** a) If A is a subset of C and B is a subset of D, then A + B is a subset of C + D. --- ### Explanation This question involves understanding the concept of subsets and set operations. You are required to analyze the given statement and determine whether it is true or false. If the statement is true, provide an example that supports the statement. If it is false, construct a counter-example to demonstrate where the statement does not hold. Key concepts to consider: - **Subset**: A set A is a subset of set B if every element of A is also an element of B. - **Set Addition**: Generally involves the union of two sets. This problem encourages logical reasoning and the application of set theory principles.
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