Let A be the sets of the letters in the world "RAIGARH" and B be the sets of the letters in the word "PRATAPGARH" then `n(A subset B)` represents.

Options

A. 7
B. 6
C. 4
D. 3

Answer

To solve the problem, we need to determine the number of elements in the set \( A \) that are also present in the set \( B \). Let's break this down step by step.

### Step 1: Identify the sets \( A \) and \( B \)

1. **Set \( A \)**: The letters in the word "RAIGARH".
- The unique letters in "RAIGARH" are: \( R, A, I, G, H \).
- Therefore, \( A = \{ R, A, I, G, H \} \).

2. **Set \( B \)**: The letters in the word "PRATAPGARH".
- The unique letters in "PRATAPGARH" are: \( P, R, A, T, G, H \).
- Therefore, \( B = \{ P, R, A, T, G, H \} \).

### Step 2: Find the intersection of sets \( A \) and \( B \)

To find \( n(A \subset B) \), we need to identify the common elements between sets \( A \) and \( B \).

- **Common elements**:
- \( R \) is in both \( A \) and \( B \).
- \( A \) is in both \( A \) and \( B \).
- \( G \) is in both \( A \) and \( B \).
- \( H \) is in both \( A \) and \( B \).
- \( I \) is not in \( B \), so we do not include it.

Thus, the common elements are \( R, A, G, H \).

### Step 3: Count the number of common elements

Now we count the elements in the intersection:

- The common elements are \( \{ R, A, G, H \} \).
- The number of elements in this intersection is \( 4 \).

### Conclusion

Therefore, \( n(A \subset B) = 4 \).