My definition of a core task is a task that a large number of end users would expect to be able to perform with a specific device, web page, or system.
A core task hence does not have to be a task that your users are already performing in your product. A core task can be a task that your users would like to perform, but where no solutions—or at least no adequate solutions—are yet available. A core task is hence any task that users expect to be able to perform with your product. It is important to emphasize that core tasks are defined by the users.
Here are some examples of wrong-headed thinking: