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diagram describing the following set by shading in the appropriate region: (A' n B) UC Draw a venn

diagram describing the following set by shading in the appropriate region: (A' n B) UC Draw a venn

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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**Instructions for Venn Diagram Representation** Draw a Venn diagram describing the following set by shading in the appropriate region: \((A' \cap B) \cup C\). **Explanation:** 1. **Venn Diagram Components:** - Three overlapping circles labeled A, B, and C. - The universal set is represented by the region outside all circles. 2. **Set Description:** - \(A'\) represents the complement of set A, meaning all areas outside circle A. - \(B\) is the area inside circle B. - \(A' \cap B\) is the area where the complement of A overlaps with B, i.e., the part of B that does not overlap with A. - \(C\) is the area inside circle C. 3. **Shading:** - Shade the region that represents \((A' \cap B) \cup C\). - This includes: - The part of circle B that does not include any part of circle A. - The entirety of circle C. - Ensure no areas that are part of both A and B are shaded unless they are also within C. By following these instructions, you will create an accurate Venn diagram representation of the given set expression.
Transcribed Image Text:**Instructions for Venn Diagram Representation** Draw a Venn diagram describing the following set by shading in the appropriate region: \((A' \cap B) \cup C\). **Explanation:** 1. **Venn Diagram Components:** - Three overlapping circles labeled A, B, and C. - The universal set is represented by the region outside all circles. 2. **Set Description:** - \(A'\) represents the complement of set A, meaning all areas outside circle A. - \(B\) is the area inside circle B. - \(A' \cap B\) is the area where the complement of A overlaps with B, i.e., the part of B that does not overlap with A. - \(C\) is the area inside circle C. 3. **Shading:** - Shade the region that represents \((A' \cap B) \cup C\). - This includes: - The part of circle B that does not include any part of circle A. - The entirety of circle C. - Ensure no areas that are part of both A and B are shaded unless they are also within C. By following these instructions, you will create an accurate Venn diagram representation of the given set expression.
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