To answer this question, you need to have knowledge about the ps command in Linux.
Let's go through each option to understand why it is correct or incorrect:
Option A) ps -a - This option displays information about all processes running on the system, regardless of whether they have a terminal or not. This option is incorrect.
Option B) ps - This option displays information about currently running processes with a terminal. This option is incorrect.
Option C) ps -x - This option displays information about all processes without a controlling terminal. This option is correct.
Option D) ps -f - This option displays detailed information about currently running processes, including the parent-child relationship. This option is incorrect.
The correct answer is C) ps -x. This option is correct because it specifically shows information about processes without terminals.