The set described by \( \{n \in \mathbb{N} : 7 \leq n < 19\} \) represents all natural numbers \( n \) that are greater than or equal to 7 and less than 19.

Since \( n \in \mathbb{N} \), this means \( n \) must be a natural number, i.e., a positive integer. Therefore, the set can be written as:

\[
\{7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18\}
\]

This is the complete set of natural numbers between 7 and 19 (inclusive of 7, but excluding 19).

Would you like further details or have any questions?

Here are five related questions for further exploration:
1. What is the cardinality (size) of this set?
2. How would the set change if \( n \in \mathbb{Z} \) (integers) instead of \( \mathbb{N} \)?
3. What would the set be if the condition was \( 7 < n < 19 \)?
4. How do we represent the same set using set-builder notation for even numbers only?
5. What if the inequality was \( 7 \leq n \leq 19 \)? How would that affect the set?

**Tip:** When working with set-builder notation, always pay attention to the type of numbers involved, like natural numbers (\( \mathbb{N} \)) or integers (\( \mathbb{Z} \)), as this determines what elements belong to the set.

Explore the set of natural numbers where 7 ≤ n < 19, including how to interpret set-builder notation and inequalities. This lesson is suitable for students in Grades 6-8 and covers key concepts in set theory and natural numbers.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation