Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama},
A = {Physics, Psychology, French, English},

B = {Math, Drama, Chemistry, French, English},
and
C = {History, Psychology, Chemistry}.
Find the following.
n(B ∪ C)

To find \( n(B \cup C) \), we need to determine the number of elements in the union of sets \( B \) and \( C \). The union of two sets contains all the elements from both sets without repeating any element.

### Given sets:
- \( B = \{ \text{Math}, \text{Drama}, \text{Chemistry}, \text{French}, \text{English} \} \)
- \( C = \{ \text{History}, \text{Psychology}, \text{Chemistry} \} \)

### Union of \( B \) and \( C \) (\( B \cup C \)):
\[ B \cup C = \{ \text{Math}, \text{Drama}, \text{Chemistry}, \text{French}, \text{English}, \text{History}, \text{Psychology} \} \]

### Counting the elements:
Now, count the distinct elements in \( B \cup C \):

\[ n(B \cup C) = 7 \]

So, \( n(B \cup C) = 7 \).

Would you like more details or have any other questions?

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Here are 5 related questions to expand your understanding:

1. How would you find \( n(A \cap B) \), the number of elements in the intersection of sets \( A \) and \( B \)?
2. What is \( n(A \cup B) \), the number of elements in the union of sets \( A \) and \( B \)?
3. How can you find the number of elements in \( B \setminus C \)?
4. What is the number of elements in \( A \cup C \)?
5. How would you determine if the union \( A \cup B \cup C \) contains all elements in \( U \)?

**Tip:** To avoid counting the same element multiple times when finding the union of sets, list all elements only once.

Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama}, A = {Physics, Psychology, French, English}, B = {Math, Drama, Chemistry, French, English}, and C = {History, Psychology, Chemistry}. Find the following. n(B ∪ C)

Discover how to find n(B ∪ C) by determining the number of elements in the union of two sets B and C. This example explores set theory concepts, including the union theorem, and is suitable for students in Grades 9-12.

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