If S={x|x is a letter in the AHMEDABAD}, then the cardinal number of S is

Options

A. 9
B. 8
C. 7
D. 6

Answer

To find the cardinal number of the set \( S = \{ x \mid x \text{ is a letter in the word "AHMEDABAD"} \} \), we will follow these steps:

### Step 1: Identify the letters in the word "AHMEDABAD"
The first step is to write down all the letters in the word "AHMEDABAD".

- The letters are: A, H, M, E, D, A, B, A, D.

### Step 2: List the unique letters
Next, we need to identify the unique letters in the word. This means we will only count each letter once, even if it appears multiple times.

- From the letters identified, we can see that:
- A appears 3 times
- H appears 1 time
- M appears 1 time
- E appears 1 time
- D appears 2 times
- B appears 1 time

So the unique letters are: A, H, M, E, D, B.

### Step 3: Count the unique letters
Now, we will count the unique letters we have identified.

- The unique letters are: A, H, M, E, D, B.
- Therefore, the total number of unique letters is 6.

### Step 4: Conclusion
The cardinal number of the set \( S \) is the count of unique letters, which is 6.

Thus, the cardinal number of \( S \) is **6**.

---