How do you determine the union of two sets?

To determine the union of two sets, you combine all the elements from both sets, ensuring that each element is included only once. The union of two sets \( A \) and \( B \) is denoted by \( A \cup B \) and includes all elements that are in \( A \), in \( B \), or in both \( A \) and \( B \).

Here are the steps to determine the union of two sets:

1. **List All Elements**: Write down all the elements in set \( A \).
2. **Include Elements from \( B \)**: Add all the elements from set \( B \), but only include elements that are not already listed.
3. **Combine and Remove Duplicates**: Ensure that the final list of elements does not contain duplicates.

### Example
Let's say we have two sets:
- \( A = \{1, 2, 3\} \)
- \( B = \{3, 4, 5\} \)

To find \( A \cup B \):

1. List all elements in \( A \): \(\{1, 2, 3\}\)
2. Include all elements from \( B \): \(\{1, 2, 3, 4, 5\}\)
3. Remove duplicates: The union is \(\{1, 2, 3, 4, 5\}\)

### Visualizing with Venn Diagram
In a Venn diagram, the union is represented by the area covered by both circles corresponding to the sets \( A \) and \( B \).

### Key Points
- The union includes every element from both sets without repetition.
- If an element is present in both sets, it is still only listed once in the union.
- The union operation is commutative, meaning \( A \cup B = B \cup A \).

Would you like more details or have any questions?

Here are some questions you might want to ask next:
1. What is the difference between union and intersection of sets?
2. Can you explain the difference between union and complement of sets?
3. How do you determine the intersection of two sets?
4. What are some properties of set operations?
5. Can you provide more examples of set operations?

**Tip:** When dealing with sets, always double-check that each element is listed only once in the union to avoid duplicates.

Explore how to determine the union of two sets (A ∪ B) with a detailed step-by-step guide. Learn about set theory, union operation, and Venn diagrams. Suitable for students in Grades 9-12.

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