Let's determine 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: $B = \{1, 3, 5, 7\}$ $C = \{7, 8, 9, 10\}$

The union $B \cup C$ is: $B \cup C = \{1, 3, 5, 7, 8, 9, 10\}$

(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: $B = \{1, 3, 5, 7\}$ $C = \{7, 8, 9, 10\}$

The intersection $B \cap C$ is: $B \cap C = \{7\}$

Answers:

• (a) $B \cup C = \{1, 3, 5, 7, 8, 9, 10\}$
• (b) $B \cap C = \{7\}$

Do you have any questions or would you like more details? Here are some related questions that might interest you:

1. How do you find the difference between two sets?
2. What does the complement of a set represent?
3. Can two sets have an empty intersection? What does that imply?
4. How can you use set notation to describe the union of multiple sets?
5. What are the properties of union and intersection in set theory?

Tip: Always remember that the union of two sets includes all elements from both sets without repetition, while the intersection only includes the elements common to both.