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.