\begin{tabular}{l} Question \\ Which of the following correctly describes the set \( \{2 n \mid n \in \mathbb{Z}\} \) ? \\ Select the correct answer below: \\ The set of all odd integers \\ The set of all integers greater than 2 . \\ The set of all real numbers greater than 2. \\ The set of all even integers. \\ \hline\end{tabular}

The set \( \{2 n \mid n \in \mathbb{Z}\} \) is the set of all even integers. This is because for any integer \( n \), multiplying by 2 results in an even number. Thus, whether \( n \) is positive, negative, or zero, the output will always be an even integer like -4, 0, or 10. If you're learning about set notation, remember that understanding the operations involved helps clarify what each set represents. For example, knowing that \( \mathbb{Z} \) represents all integers and that multiplying by 2 generates even results can be a handy shortcut for identifying similar expressions!