e Venn diagram shows sets A, B, C, and the universal set U. made (AUB)'n C' on the Venn diagram. U B. Explanation Check 19 A 1 Español ! As Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility ■ Ti

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Where do I shade?

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### Shading a Venn Diagram with 3 Sets: Unions, Intersections, and Complements

#### Description

The Venn diagram shows sets \( A \), \( B \), \( C \), and the universal set \( U \). Shade \( (A \cup B') \cap C' \) on the Venn diagram.

#### Diagram Explanation

In the Venn diagram:

- The universal set \( U \) is represented by the rectangular boundary.
- Sets \( A \), \( B \), and \( C \) are represented by three overlapping circles within \( U \).
- \( A \) is the circle labeled \( A \).
- \( B \) is the circle labeled \( B \).
- \( C \) is the circle labeled \( C \).

The goal is to shade the region that satisfies the expression \( (A \cup B') \cap C' \).

1. **Understanding \( B' \)**:
   - \( B' \) is the complement of set \( B \), which includes all regions outside circle \( B \).

2. **Understanding \( A \cup B' \)**:
   - \( A \cup B' \) is the union of set \( A \) and the complement of set \( B \). This means any region that is in circle \( A \) or outside circle \( B \).

3. **Understanding \( C' \)**:
   - \( C' \) is the complement of set \( C \), which includes all regions outside circle \( C \).

4. **Finding \( (A \cup B') \cap C' \)**:
   - This is the intersection of the union \( (A \cup B') \) with the complement \( C' \). Therefore, only the regions that satisfy both conditions simultaneously (either in \( A \) or outside \( B \)) and (outside \( C \)) should be shaded.

To shade the appropriate region in the Venn diagram, identify the areas that fall outside circle \( C \) and also belong to either circle \( A \) or are outside circle \( B \).

---

##### Interactive Elements

- **Pencil Icon**: Click to start shading the desired region.
- **Eraser Icon**: Click to erase any mistakes while shading.
- **Undo Icon**: Click to undo the previous action.
- **Help Icon**: Click for more detailed instructions on using the shading
Transcribed Image Text:--- ### Shading a Venn Diagram with 3 Sets: Unions, Intersections, and Complements #### Description The Venn diagram shows sets \( A \), \( B \), \( C \), and the universal set \( U \). Shade \( (A \cup B') \cap C' \) on the Venn diagram. #### Diagram Explanation In the Venn diagram: - The universal set \( U \) is represented by the rectangular boundary. - Sets \( A \), \( B \), and \( C \) are represented by three overlapping circles within \( U \). - \( A \) is the circle labeled \( A \). - \( B \) is the circle labeled \( B \). - \( C \) is the circle labeled \( C \). The goal is to shade the region that satisfies the expression \( (A \cup B') \cap C' \). 1. **Understanding \( B' \)**: - \( B' \) is the complement of set \( B \), which includes all regions outside circle \( B \). 2. **Understanding \( A \cup B' \)**: - \( A \cup B' \) is the union of set \( A \) and the complement of set \( B \). This means any region that is in circle \( A \) or outside circle \( B \). 3. **Understanding \( C' \)**: - \( C' \) is the complement of set \( C \), which includes all regions outside circle \( C \). 4. **Finding \( (A \cup B') \cap C' \)**: - This is the intersection of the union \( (A \cup B') \) with the complement \( C' \). Therefore, only the regions that satisfy both conditions simultaneously (either in \( A \) or outside \( B \)) and (outside \( C \)) should be shaded. To shade the appropriate region in the Venn diagram, identify the areas that fall outside circle \( C \) and also belong to either circle \( A \) or are outside circle \( B \). --- ##### Interactive Elements - **Pencil Icon**: Click to start shading the desired region. - **Eraser Icon**: Click to erase any mistakes while shading. - **Undo Icon**: Click to undo the previous action. - **Help Icon**: Click for more detailed instructions on using the shading
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