Answer, whether the following statements are true or false. Give reasons.
The set of even natural numbers less than 21 and the set of odd natural numbers less than 21 are equivalent sets.

Answer

To determine whether the set of even natural numbers less than 21 and the set of odd natural numbers less than 21 are equivalent sets, we will follow these steps:

### Step 1: Define the Sets
- **Set A**: The set of even natural numbers less than 21.
- **Set B**: The set of odd natural numbers less than 21.

### Step 2: List the Elements of Set A
The even natural numbers less than 21 are:
- 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

So, we can write:
- **Set A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}**

### Step 3: List the Elements of Set B
The odd natural numbers less than 21 are:
- 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

So, we can write:
- **Set B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}**

### Step 4: Count the Elements in Each Set
- Count the elements in Set A:
- There are 10 elements in Set A.

- Count the elements in Set B:
- There are also 10 elements in Set B.

### Step 5: Determine if the Sets are Equivalent
Two sets are considered equivalent if they have the same number of elements. Since both Set A and Set B have 10 elements, we conclude that:
- Set A and Set B are equivalent sets.

### Final Answer
The statement is **True**. The set of even natural numbers less than 21 and the set of odd natural numbers less than 21 are equivalent sets because they both contain the same number of elements (10).

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