How to deal with arrogant e-mail of a student I have sent the solutions of some assignments to the students of my class.

One of my students sent me a message that reads as follows (not greeting or anything, no closing, just the following): 


  The proposed solution of Exercise X is obviously wrong because of reason blah blah. An appropriate solution to your exercise would be such and such.


Now, the student in essence is actually correct: there is a slight error (but it does not alter the essence of the solution). It is just a small wording issue that might raise some confusion (but the calculations are clear).

What troubles me is the attitude, which I found kind of offensive (but I might be wrong). 

Is it appropriate a student to behave like that? What would be the right approach to deal with this student?

I answered as politely as I could that the student is right, thanked the student for spotting it, and updated the solution manual. But I feel that the student would create similar issues and make similar comments if some typos are found in subsequent notes.

Note: The actual problem might be that the student might start bad-mouthing me to other students/professors and this might negatively influence other students in believing that I am doing a bad job and consequently this could be reflected on my teaching evaluations (given also that I try to get tenured). Maybe I am paranoid (hope so!), but in relatively small classes where everyone knows each other, the power of bad-mouthing can be great. I want a way to (a) avoid confrontation and (b) make it clear that these issues are completely minor (they are) and not worthy of such aggressive (which they might not be, but I do not want to take chances) messages.
How to deal with this?


Dear [student],

Thank you for pointing this out. 

[1 or 2 more sentences of explanation]

Sincerely, [your name].


  What troubles me is the attitude, which I found it kind of offensive (but I might be wrong).


Maybe the email is offensive, or maybe the student just wrote an email from their phone. Maybe they are actively trying to be a jerk, or maybe they just don't know how to behave properly. Maybe they are just trying to be a troll. In all those cases, I have found the best way is just to not engage and write a neutral response that does not comment on the perceived rudeness.


If it's just a regular student writing an email from the phone, this does not create a conflict out of thin air.
If it's a jerk or troll, this does little to satisfy their hunger for drama.
If it's a student without manners, well, you are not their parent - don't make it your job to educate them on proper email etiquette.


What I certainly would not recommend is "inviting" them into your office for some sort of explanation, just for writing a factually correct but unfriendly email. You are, again, at worst creating a conflict where there is none, and at best spending significant energy trying to educate a fellow adult on basics of etiquette.


  But I feel that the student would create same issues in case some typo is found in the subsequent notes and make similar comments.


So what? If they have a real concern, address them. If they make things up to feel important, either ignore the email or tell them that you do not see the issue.