Select the correct answer below: \( \begin{array}{l}\{n \mid 2 n+1 \in \mathbb{Z}\} \\ \bigcirc\{2 n \mid n \in \mathbb{Z}\} \\ \bigcirc\{2 n+1 \mid x \in \mathbb{Z}\} \\ \bigcirc\{2 n+1 \mid n \in \mathbb{Z}\}\end{array} \)
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Bonus Knowledge
The set you're looking for is \( \{2 n+1 \mid n \in \mathbb{Z}\} \). This set defines all odd integers, which is generated by taking an integer \( n \) and applying the expression \( 2 n + 1 \). Each integer \( n \) will produce a distinct odd integer, thus perfectly representing the set of all odd numbers. On the other hand, \( \{2 n \mid n \in \mathbb{Z}\} \) generates even integers, \( \{2 n + 1 \mid x \in \mathbb{Z}\} \) has a typo where \( x \) should be \( n \), and those represent the same odd integer set as before. Just a little confusion to watch out for!
