Park Rodriquez
05/16/2023 · Primary School

\( A=\{3 x: x \in \) sets using set buitder method Write the following set \( A=\{1,3, \ldots, \cdots\} \)

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To express the set \( A = \{1, 3, \ldots\} \) using the set builder notation, we first need to identify the pattern in the elements of the set. The elements appear to be the odd positive integers. The set can be defined as follows: \[ A = \{ x \in \mathbb{Z}^+ : x \text{ is odd} \} \] Alternatively, since the odd positive integers can also be expressed in terms of a formula, we can write: \[ A = \{ 2n - 1 : n \in \mathbb{Z}^+ \} \] where \( n \) is a positive integer (i.e., \( n = 1, 2, 3, \ldots \)). This notation captures all the odd positive integers starting from 1.

Quick Answer

\( A = \{ 2n - 1 : n \in \mathbb{Z}^+ \} \)
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