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!