https://r2.erweima.ai/mathbot/image/1726420626683fpp6l5ja.jpg

Let's analyze the question:

We have two sets:
- \( A = \{1, 3, 5, 7, 9, 11\} \)
- \( B = \{1, 5, 11\} \)

The statements are:

1. \( A \cap B = \{1, 3, 5, 7, 9, 11\} \) (Intersection of A and B)
2. \( A \cup B = \{1, 5, 11\} \) (Union of A and B)
3. \( A - B = \{3, 7, 9\} \) (Difference between A and B)

Now, let's evaluate each statement:

### Statement I: Intersection
The intersection of two sets \( A \cap B \) contains elements that are in both \( A \) and \( B \). Since \( B = \{1, 5, 11\} \), the elements common to both sets are \( \{1, 5, 11\} \). 
Thus, the correct intersection is:
\[ A \cap B = \{1, 5, 11\} \]

This means **Statement I is false**.

### Statement II: Union
The union \( A \cup B \) contains all elements that are in either \( A \) or \( B \). So:
\[ A \cup B = \{1, 3, 5, 7, 9, 11\} \]

This means **Statement II is false**.

### Statement III: Difference
The difference \( A - B \) contains elements that are in \( A \) but not in \( B \). So:
\[ A - B = \{3, 7, 9\} \]

This means **Statement III is correct**.

### Conclusion:
The correct answer is **D**, as only Statement III is true.

Do you want more details or have any questions? Here are 5 related questions:

1. What is the definition of the union of two sets?
2. How do you find the difference between two sets?
3. Can the intersection of two sets ever be larger than either set?
4. What is the relationship between the union and intersection of sets?
5. How can we verify if two sets are disjoint?

**Tip:** When calculating intersections, always look for common elements between the sets.

Se A = {1, 3, 5, 7, 9, 11} e B = {1, 5, 11}, então A ∩ B, A ∪ B, e A - B. Qual afirmação é correta?

Understand how to perform set operations such as intersection, union, and difference with sets A = {1, 3, 5, 7, 9, 11} and B = {1, 5, 11}. Learn which operations result in valid outputs and solve common set theory problems suitable for Grades 8-10.

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