Find the indicated set if given the following. (Enter your answer as a set. Enter EMPTY for the empty set.)
A = {1, 2, 3, 4, 5, 6, 7}      B = 
{2, 4, 6, 8}
      
C = {7, 8, 9, 10}
 

(a)    B ∪ C 
  

(b)    B ∩ C 
  

Let's find the indicated sets:

### (a) \( B \cup C \)
The union of sets \( B \) and \( C \) is the set of all elements that are in either \( B \), \( C \), or both.

Given:
\[ B = \{2, 4, 6, 8\} \]
\[ C = \{7, 8, 9, 10\} \]

The union \( B \cup C \) is:
\[ B \cup C = \{2, 4, 6, 7, 8, 9, 10\} \]

### (b) \( B \cap C \)
The intersection of sets \( B \) and \( C \) is the set of all elements that are common to both \( B \) and \( C \).

Given:
\[ B = \{2, 4, 6, 8\} \]
\[ C = \{7, 8, 9, 10\} \]

The intersection \( B \cap C \) is:
\[ B \cap C = \{8\} \]

### Answers:
- (a) \( B \cup C = \{2, 4, 6, 7, 8, 9, 10\} \)
- (b) \( B \cap C = \{8\} \)

Would you like more details on this problem or have any questions? Here are some related questions you might find helpful:

1. What is the difference between union and intersection of sets?
2. How do you find the complement of a set?
3. What does it mean for a set to be a subset of another?
4. How can you visualize the union and intersection of sets using Venn diagrams?
5. What are some real-life examples where union and intersection of sets are used?

**Tip:** The union of two sets combines all distinct elements, while the intersection captures only the elements they share.

Explore the union and intersection of sets B and C with detailed explanations and examples. Understand how to find the union (B ∪ C) and intersection (B ∩ C) of sets using set theory principles. Suitable for Grades 7-9 students.

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