Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama}, 
A = {Physics, Math, English, Chemistry},
 
B = {History, Drama, French, English, Chemistry},
 and 
C = {Psychology, Math, French}.
 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 includes all distinct elements from both sets. Let's break this down:

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

### Step 1: Find the union \( B \cup C \)
The union includes all unique elements from both \( B \) and \( C \):

\[
B \cup C = \{\text{History}, \text{Drama}, \text{French}, \text{English}, \text{Chemistry}, \text{Psychology}, \text{Math}\}
\]

### Step 2: Count the elements in \( B \cup C \)
The distinct elements in \( B \cup C \) are:

\[
B \cup C = \{\text{History}, \text{Drama}, \text{French}, \text{English}, \text{Chemistry}, \text{Psychology}, \text{Math}\}
\]

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

### Final Answer:
\[
n(B \cup C) = 7
\]

Would you like a detailed explanation of how we found the union or any other questions?

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**Related questions:**
1. What is \( n(A \cup B) \)?
2. Find \( n(B \cap C) \).
3. What is \( n(A \cap C) \)?
4. How many elements are in \( B \setminus C \)?
5. Find \( n(U \setminus (A \cup B)) \).

**Tip:** When calculating a union, make sure to avoid double-counting elements that appear in both sets!

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

Explore how to find the union of sets B and C with a detailed solution to the problem. This example covers set theory, union of sets, and cardinality, suitable for students in Grades 9-11. The solution involves determining the distinct elements in both sets and calculating n(B ∪ C).

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