Find the cardinal number of the following sets :
A={x:x is a factor of 18}

Answer

To find the cardinal number of the set \( A = \{ x : x \text{ is a factor of } 18 \} \), we will follow these steps:

### Step 1: Identify the factors of 18
Factors of a number are the integers that can be multiplied together to produce that number. We will find all pairs of integers that multiply to give 18.

- The pairs are:
- \( 1 \times 18 = 18 \)
- \( 2 \times 9 = 18 \)
- \( 3 \times 6 = 18 \)

### Step 2: List all distinct factors
From the pairs identified, we can list all the distinct factors of 18:
- \( 1 \)
- \( 2 \)
- \( 3 \)
- \( 6 \)
- \( 9 \)
- \( 18 \)

Thus, the set \( A \) can be written in roster form as:
\[ A = \{ 1, 2, 3, 6, 9, 18 \} \]

### Step 3: Count the number of distinct elements
Now, we count the number of distinct elements in the set \( A \):
- The elements are \( 1, 2, 3, 6, 9, 18 \).

Counting these, we find there are 6 distinct elements.

### Step 4: State the cardinal number
The cardinal number of the set \( A \) is the total number of distinct elements, which we have found to be:
\[ \text{Cardinal number} = 6 \]

### Final Answer
The cardinal number of the set \( A \) is \( 6 \).

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