If `A = {2,4,6,8,10}` and `B= {1,3,5,7,9}` then write `A cup B ` in the set builder form .

Answer

To solve the problem of writing \( A \cup B \) in set builder form, we will follow these steps:

### Step 1: Identify the sets
We have two sets:
- \( A = \{2, 4, 6, 8, 10\} \) (which contains even numbers)
- \( B = \{1, 3, 5, 7, 9\} \) (which contains odd numbers)

### Step 2: Find the union of the sets
The union of two sets \( A \) and \( B \), denoted as \( A \cup B \), includes all elements that are in either set. Thus, we combine the elements of both sets:
- \( A \cup B = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \)

### Step 3: Write the union in set builder form
Set builder form is a way to describe a set by stating the properties that its members must satisfy.

In this case, the elements of \( A \cup B \) are all the natural numbers from 1 to 10. Therefore, we can express this in set builder notation as:
\[ A \cup B = \{ x \, | \, x \text{ is a natural number and } x \leq 10 \} \]

### Final Answer
Thus, the set \( A \cup B \) in set builder form is:
\[ A \cup B = \{ x \, | \, x \text{ is a natural number and } x \leq 10 \} \]

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