A={1,3,5... } Describe this using set builder method

The set \( A = \{1, 3, 5, \dots \} \) represents the set of all odd positive integers. To express this set using **set-builder notation**, you describe the elements of the set in terms of a defining property. The set \( A \) can be described as follows:

\[
A = \{ x \mid x = 2n - 1, n \in \mathbb{N} \}
\]

### Explanation:
- \( x \) represents the elements of the set.
- \( x = 2n - 1 \) describes the general form of odd integers.
- \( n \in \mathbb{N} \) means that \( n \) is a natural number (positive integers starting from 1).

This set-builder notation states that \( A \) contains all numbers that can be expressed as \( 2n - 1 \) where \( n \) is a natural number.

Do you want further clarification on any part of this?

Here are some questions for practice:
1. How would you describe the set of even numbers using set-builder notation?
2. Can you describe the set of all multiples of 3 using set-builder notation?
3. How would you represent the set of perfect squares using set-builder notation?
4. How would you describe the set \( B = \{2, 4, 6, \dots \} \) using set-builder notation?
5. Can you represent the set of prime numbers using set-builder notation?

**Tip:** Set-builder notation is a powerful way to describe sets concisely using logical conditions or equations.

Learn how to describe the set A = {1, 3, 5, ...}, which contains all odd positive integers, using set-builder notation. This lesson explains the concept of set-builder notation with examples and is suitable for students in Grades 6-8.

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