In a Venn Diagram, a set is represented by a circle (or other closed geometric figure). Anything inside the circle is an element of the set, and anything outside the circle is not an element of the set. The picture represents two sets A (solid line) and B (dashed line). B. Determine whether the statements are true (T) or false (F). y € A y € B | 1 € ANB| we B 2 € AUB| AC B T or F T or F T or F T or F T or F T or F N.

Advanced Engineering Mathematics
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**Venn Diagram Explanation**

A Venn Diagram is used to visually represent the relationships between different sets. Each set is depicted by a circle or another closed geometric figure. Elements that belong to a set are placed inside the circle, whereas elements that do not belong to the set are positioned outside the circle.

In the provided diagram, the sets \( A \) and \( B \) are illustrated. Set \( A \) is represented by a solid line circle, and set \( B \) is represented by a dashed line circle. 

### Diagram Description

- **Elements and their Locations:**
  - \( w \) is located outside both circles (\( A \) and \( B \)).
  - \( x \) is inside circle \( A \) but outside circle \( B \).
  - \( y \) is within the overlapping area of circles \( A \) and \( B \).
  - \( z \) is inside circle \( B \) but outside circle \( A \).

### Statements to Evaluate

The following table contains statements to determine if they are true (T) or false (F) based on the positions of elements in the Venn Diagram:

1. \( y \in A \)
2. \( y \in B \)
3. \( x \in A \cap B \)
4. \( w \in \bar{B} \)
5. \( z \in A \cup B \)
6. \( A \subseteq B \)

**Instructions:** For each statement, mark T or F based on the diagram.
Transcribed Image Text:**Venn Diagram Explanation** A Venn Diagram is used to visually represent the relationships between different sets. Each set is depicted by a circle or another closed geometric figure. Elements that belong to a set are placed inside the circle, whereas elements that do not belong to the set are positioned outside the circle. In the provided diagram, the sets \( A \) and \( B \) are illustrated. Set \( A \) is represented by a solid line circle, and set \( B \) is represented by a dashed line circle. ### Diagram Description - **Elements and their Locations:** - \( w \) is located outside both circles (\( A \) and \( B \)). - \( x \) is inside circle \( A \) but outside circle \( B \). - \( y \) is within the overlapping area of circles \( A \) and \( B \). - \( z \) is inside circle \( B \) but outside circle \( A \). ### Statements to Evaluate The following table contains statements to determine if they are true (T) or false (F) based on the positions of elements in the Venn Diagram: 1. \( y \in A \) 2. \( y \in B \) 3. \( x \in A \cap B \) 4. \( w \in \bar{B} \) 5. \( z \in A \cup B \) 6. \( A \subseteq B \) **Instructions:** For each statement, mark T or F based on the diagram.
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In the given Venn Diagram, a set is represented by a circle. Anything inside the circle is an element of the set , and anything outside of the set is not an element of the set. And the given picture represents two sets A (solid line) and B (dashed line).

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