Write the set {3,6,9,12} in set Builder Form.

Answer

To write the set {3, 6, 9, 12} in set builder form, we can follow these steps:

### Step 1: Identify the elements of the set
The elements of the set are 3, 6, 9, and 12. We can observe that these numbers are multiples of 3.

### Step 2: Determine the pattern
Notice that each element can be expressed as 3 times a positive integer. Specifically:
- 3 = 3 × 1
- 6 = 3 × 2
- 9 = 3 × 3
- 12 = 3 × 4

### Step 3: Define the variable
Let’s define a variable \( x \) that represents the positive integers. In this case, \( x \) can take on the values 1, 2, 3, and 4.

### Step 4: Write the set builder notation
Using the observations from the previous steps, we can express the set in set builder form. The set can be defined as:
\[ A = \{ 3x \mid x \in \mathbb{Z}^+, 1 \leq x \leq 4 \} \]
where \( \mathbb{Z}^+ \) denotes the set of positive integers.

### Final Answer:
Thus, the set {3, 6, 9, 12} in set builder form is:
\[ A = \{ 3x \mid x \in \mathbb{Z}^+, 1 \leq x \leq 4 \} \]

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