Write the following sets in the set builder form :
`B={7,14,21,28, . . . }`

Answer

To write the set \( B = \{ 7, 14, 21, 28, \ldots \} \) in set builder form, we can follow these steps:

### Step 1: Identify the Pattern
The elements of the set \( B \) are 7, 14, 21, 28, and so on. We can observe that these numbers are all multiples of 7.

**Hint:** Look for a common factor or a rule that defines the elements of the set.

### Step 2: Define the Variable
Let’s denote the elements of the set with a variable, say \( x \).

**Hint:** Choose a variable that will represent the elements of the set.

### Step 3: Express the Condition
Since all the numbers in the set are multiples of 7, we can express this condition mathematically. A number \( x \) is a multiple of 7 if there exists an integer \( n \) such that \( x = 7n \).

**Hint:** Think about how you can express the relationship between the variable and the multiples.

### Step 4: Write in Set Builder Notation
Now, we can write the set in set builder form. The set builder form will be:
\[ B = \{ x \mid x = 7n, \, n \in \mathbb{Z}^+ \} \]
Here, \( \mathbb{Z}^+ \) denotes the set of positive integers (1, 2, 3, ...).

**Hint:** Use the notation \( \{ x \mid \text{condition} \} \) to define the set based on the identified condition.

### Final Answer
Thus, the set \( B \) in set builder form is:
\[ B = \{ x \mid x = 7n, \, n \in \mathbb{Z}^+ \} \]