Without. "Task Manager" is the name of a program, not a manager of tasks. You are tempted to use the article at all only because of the descriptive name.
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Cynthia3754I prefer the definite article. It just seems more natural to me. I taught computers for years and I always used the definite article. I probably picked up the habit of from the books I studied.You mean just for "Task Manager", right? You could probably catch me saying the article, truth be told, but I still recommend not writing it.
MUSCOVITEI understand either version ( with and without 'the' before Task Manager) is grammatical? Anyway, which version would YOU prefer anf WHY?I prefer 'the Task Manager' because I like the sound of it. It sounds right to me.