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.