What is the relation between An B and AnB ? Justify your

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Question:**

What is the relation between \( A \cap \overline{B} \) and \( \overline{A} \cap B \)? Justify your answer.

**Explanation:**

The question involves set theory, particularly focusing on the intersection of a set with the complement of another set. 

- \( A \cap \overline{B} \): This represents the set of elements that are in \( A \) but not in \( B \).
- \( \overline{A} \cap B \): This represents the set of elements that are not in \( A \) but are in \( B \).

The question asks you to explore and describe the relationship between these two sets, providing justification based on set theory principles.
Transcribed Image Text:**Question:** What is the relation between \( A \cap \overline{B} \) and \( \overline{A} \cap B \)? Justify your answer. **Explanation:** The question involves set theory, particularly focusing on the intersection of a set with the complement of another set. - \( A \cap \overline{B} \): This represents the set of elements that are in \( A \) but not in \( B \). - \( \overline{A} \cap B \): This represents the set of elements that are not in \( A \) but are in \( B \). The question asks you to explore and describe the relationship between these two sets, providing justification based on set theory principles.
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