https://file.aiquickdraw.com/mathbot/file/1727934260159v71pnbkn.jpg

Let's go through the Venn diagram shown in the image and solve the given questions one by one.

### Given:
- The universal set \( U \) is divided into two subsets \( A \) and \( B \), with their corresponding elements marked in the diagram.
- Elements labeled as \( a, b, c, d, e, f, g \).

From the Venn diagram:
- \( A \) is the set containing the elements \( a, c, d \).
- \( B \) is the set containing the elements \( b, c, e \).
- The universal set \( U \) contains \( a, b, c, d, e, f, g \).

### Let's answer each question:

1. **\( U \):**  
   The universal set contains all the elements present in the diagram.  
   \( U = \{a, b, c, d, e, f, g\} \)

2. **\( A' \cup B' \) (Complement of A union complement of B):**  
   We need to find the elements that are not in \( A \) or not in \( B \).  
   \( A' = \{b, e, f, g\} \) (elements not in \( A \))  
   \( B' = \{a, d, f, g\} \) (elements not in \( B \))  
   \( A' \cup B' = \{a, b, d, e, f, g\} \)

3. **\( A' \cap B' \) (Complement of A intersect complement of B):**  
   Elements that are not in \( A \) and not in \( B \).  
   \( A' \cap B' = \{f, g\} \)

4. **\( A' \cap B \) (Complement of A intersect B):**  
   Elements that are not in \( A \) but are in \( B \).  
   \( A' \cap B = \{b, e\} \)

5. **\( A \cup B' \) (A union complement of B):**  
   Elements that are in \( A \) or not in \( B \).  
   \( A \cup B' = \{a, c, d, f, g\} \)

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Let me know if you'd like any more details or explanations!

### Relative Questions:
1. What is the difference between the union and intersection of two sets?
2. How do we find the complement of a set in a universal set?
3. Can you explain the logic behind finding \( A' \cup B' \)?
4. How would the sets change if a new element was added only to \( A \)?
5. Can you show an example where \( A \cap B' \) has more elements?

### Tip:
Always double-check set complements to ensure you've included all elements outside the specific set(s).

List the elements of the following sets from the figure shown in the Venn diagram.

Learn how to perform set operations such as union, intersection, and complement using a Venn diagram. This exercise helps students understand set theory, including how to apply De Morgan's Laws. Suitable for students in Grades 8-10.

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