Final answer:
The sentence requires a verb that indicates either the ability ('can') or permission ('may') of the inspector to open and close the fireplace damper, depending on the context.
Step-by-step explanation:
The sentence in the student's question requires choosing the correct verb form to fill in the blank. The inspector, being a single third person subject, requires a singular verb in the present simple tense for actions that are generally performed. Therefore, the appropriate verb to use is either 'can' or 'may' depending on the context—if it's about the ability to do something, 'can' is proper, but if it's about the permission to do something, 'may' is more suitable. A full answer for the student's question would be: 'The inspector can open and close the damper of a fireplace if referring to the inspector's ability or 'The inspector may open and close the damper of a fireplace' if talking about permission.
The question is asking about the person who opens and closes the damper of a fireplace, which is a related topic in English. In English, we use various verb forms to talk about actions and responsibilities. In this case, the inspector is the one who performs the action of opening and closing the damper.