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The problem asks to find how many elements are in the complement of set \( A \), denoted as \( A' \), using the provided Venn diagram.

### Step-by-step solution:
1. **Elements inside set \( A \)**:
   - The diagram shows that:
     - 27 elements are in set \( A \) but not in \( B \).
     - 13 elements are in both \( A \) and \( B \) (intersection).
   - So, the total number of elements in \( A \) is \( 27 + 13 = 40 \).

2. **Elements outside set \( A \) (complement of \( A \))**:
   - The universal set \( U \) contains 109 elements (27 + 13 + 29 + 40 from the entire Venn diagram).
   - The number of elements in the complement of \( A \) would be the number of elements in the universal set minus the elements in \( A \):
     \[
     n(A') = 109 - 40 = 69
     \]

Therefore, the number of elements in \( A' \) is 69.

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Would you like more details, or do you have any other questions?

Here are 5 related questions to explore:
1. How do you calculate the complement of a set?
2. What is the intersection of sets and how is it represented?
3. How would you calculate \( B' \), the complement of set \( B \)?
4. How is the universal set used in Venn diagrams?
5. How would the result change if we added another set to the diagram?

**Tip**: Always ensure the total from all parts of the Venn diagram matches the size of the universal set when solving problems.

Refer to the Venn diagram below. How many elements are in the set A'?

Explore a step-by-step solution to finding the number of elements in the complement of set A (A') using a Venn diagram. This problem helps students understand set theory concepts, including how to calculate the complement of a set and the total number of elements in a universal set. Suitable for students in Grades 6-8.

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