Find the cardinal number of the following sets :
B = {x|x is a vowel in the word DEHRADOON}

Answer

To find the cardinal number of the set B, which consists of the vowels in the word "DEHRADOON," we can follow these steps:

### Step-by-Step Solution:

1. **Identify the word**: The word given is "DEHRADOON."

2. **List the vowels**: The vowels in the English language are A, E, I, O, U. We will look for these vowels in the word "DEHRADOON."

3. **Extract the vowels from the word**:
- From "DEHRADOON," we can identify the vowels:
- D (not a vowel)
- E (vowel)
- H (not a vowel)
- R (not a vowel)
- A (vowel)
- D (not a vowel)
- O (vowel)
- O (vowel)
- N (not a vowel)

4. **Collect the unique vowels**: The vowels we found are E, A, O. Note that the letter O appears twice, but we only count unique elements in a set.
- Therefore, the unique vowels in the set B are {E, A, O}.

5. **Count the elements in the set**: Now we count the number of unique vowels in set B.
- The unique vowels are E, A, and O, which gives us a total of 3 unique elements.

6. **Determine the cardinal number**: The cardinal number of a set is the number of elements in that set.
- Thus, the cardinal number of set B is 3.

### Final Answer:
The cardinal number of the set B is 3.

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