State whether the following sets are empty finite or infinite sets., mention the cardinal number.
{x:x is an even whole number and `x le20` }

Answer

To determine whether the set {x: x is an even whole number and x ≤ 20} is empty, finite, or infinite, and to find its cardinal number, we can follow these steps:

### Step 1: Understand the Definition of the Set
The set is defined as all even whole numbers that are less than or equal to 20.

### Step 2: Identify Even Whole Numbers
Even whole numbers are numbers that are divisible by 2 and include whole numbers starting from 0. The sequence of even whole numbers is: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

### Step 3: List the Elements of the Set
Now, we will list all the even whole numbers that are less than or equal to 20:
- 0
- 2
- 4
- 6
- 8
- 10
- 12
- 14
- 16
- 18
- 20

### Step 4: Count the Elements
Next, we count the number of elements in the set:
- The elements are: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
- There are a total of 11 elements.

### Step 5: Determine the Type of Set
Since there is a fixed number of elements (11), the set is not empty and does not go on indefinitely. Therefore, the set is a finite set.

### Step 6: State the Cardinal Number
The cardinal number of a set is the number of elements in that set. In this case, the cardinal number is 11.

### Final Statement
The set {x: x is an even whole number and x ≤ 20} is a finite set, and its cardinal number is 11.

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