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I don't see many questions explaining the difference between "can't", "may not", "mustn't" and "to be not supposed to" in modal verbs of permission on StackExchange.

I would say "you can't use this computer", "you may not use this computer", "you mustn't use this computer" and "you are not supposed to use this computer" all mean "you are not allowed to use this computer".

This is what I think but I am not sure it's correct.

"you can't use this computer" and "you may not use this computer" are more personal things. Maybe, this is my personal computer and you are not allowed to use it. "May not" is more polite than "can't".

"you mustn't use this computer" and "you are not supposed to use this computer" are more like a rule of a company or organization. Maybe, this computer in this company is special and the company's rule says only some can use it not all. However, "mustn't" is a bit stricter than "are not supposed to".

What is the difference between "you can't / may not / mustn't / are not supposed to use this computer"?

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For some, “can” necessarily implies physical impossibility.

You cannot use this computer because you do not have the password.

It sounds weird to say

You may not use this computer because you do not have the password.

Although not everyone makes the distinction in affirmative statements, it is useful in distinguishing between what is physically possible and what is permissible. And, as my example shows, the distinction is sometimes virtually mandatory in negative statements.

In affirmative statements, there is a clear-cut distinction between “must,” indicating obligation, and “may,” indicating permission. The distinction does not apply to negative statements: “obliged not to do” and “not permitted to do” clearly have the same meaning.

“Supposed to do” is a weak form of “must.”

The rules say you are supposed to be at assembly

implies that the rules literally say “you must be at assembly,” but the rules are not strictly enforced.

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I used to have a teacher who, when a pupil would ask "sir, can I go to the toilet?", would invariably respond "I have no doubt that you can, the question is whether you may." He was that kind of person.

The point is that for grammatical sticklers like my teacher, "can" refers to ability, whereas "may" refers to permission. So, "you can't use that computer" means "you are not able to"; whereas "you may not use that computer" is "you do not have permission to".

"Must not" is stronger than "may not". Whereas "may not" can have the sense of the absence of permission, "must not" implies a positive denial of permission. "Students must not use that computer".

"Supposed to" has a different sense: if someone was using the computer without permission, you might say "You're not supposed to be using that."

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