Express the set using the roster method.

{x | x∈**N**  and  30≤x<90}




To express the set \(\{x \mid x \in \mathbb{N} \text{ and } 30 \leq x < 90\}\) using the roster method, we list all the natural numbers \(x\) that satisfy \(30 \leq x < 90\). The natural numbers (denoted by **N**) are positive integers starting from 1, so we list all the natural numbers between 30 and 89 (since \(x\) must be less than 90).

Thus, the set in roster form is:

\[
\{30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89\}
\]

Would you like more details on set notation, or do you have any questions?

### Related questions:
1. What is the difference between roster method and set-builder notation?
2. How would you express the set of even numbers between 30 and 90 in roster form?
3. What if the set was defined over integers (instead of natural numbers)?
4. How do we express infinite sets using roster method?
5. What are common uses of natural numbers in set theory?

**Tip**: When writing sets in roster form, you list all distinct elements in the set, making sure no elements are repeated.

Express the set using the roster method: {x | x∈N and 30≤x<90}

Learn how to express a set of natural numbers between 30 and 89 using the roster method. This problem introduces key concepts in set theory, including the roster method and set-builder notation. Suitable for students in Grades 6-8.

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