Write the set using the roster method.

Set D is the set of positive two-digit even numbers less than 2626 that do not contain the digit 44.

To write Set \( D \), which consists of positive two-digit even numbers less than 2626 that do not contain the digit 4, using the roster method, follow these steps:

1. First, identify the range of two-digit even numbers: these are numbers between 10 and 99 that are divisible by 2.
2. Remove any numbers that contain the digit 4.

### Step-by-step process:
- The set of two-digit even numbers is:
\[ \{10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98\} \]
- Remove numbers containing the digit 4:
\[ \{10, 12, 16, 18, 20, 22, 26, 28, 30, 32, 36, 38, 50, 52, 56, 58, 60, 62, 66, 68, 70, 72, 76, 78, 80, 82, 86, 88, 90, 92, 96, 98\} \]

### Final Set D (roster method):
\[ D = \{10, 12, 16, 18, 20, 22, 26, 28, 30, 32, 36, 38, 50, 52, 56, 58, 60, 62, 66, 68, 70, 72, 76, 78, 80, 82, 86, 88, 90, 92, 96, 98\} \]

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**Related questions:**
1. What is the roster method in set theory?
2. How do we determine if a number is even?
3. How can sets be represented using set-builder notation?
4. What are other examples of sets defined by number properties?
5. How would you describe sets using intervals?

**Tip:** When using the roster method, ensure that all elements of the set are listed explicitly, and avoid duplicates!

Write the set using the roster method. Set D is the set of positive two-digit even numbers less than 100 that do not contain the digit 4.

Discover how to write Set D, consisting of positive two-digit even numbers less than 100 that do not contain the digit 4, using the roster method. This step-by-step solution is perfect for middle school students learning about sets and even numbers.

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