Практическая грамматика

Can she be waiting for us?
Неужели она нас ждет?
She cannot be waiting for us.
Не может быть, чтобы она нас ждала.
Can (could) she have said that?
Неужели она это сказала?
Could it be true?
Неужели это правда?
There could not have been such relentless unforgiveness.
Не может быть, чтобы человек мог так жестоко не прощать.
«Oh!» cried Fleur. "You could not have done it." (Galsworthy)
«О!»,– вскричала Флэр. «Не может быть, чтобы вы это сделали!»
Can she have been waiting for us all the time?
Неужели она нас все это время ждет?
They couldn't have seen us.
Не может быть, чтобы они нас видели.
In the last two examples we can easily replace could by can without any change of meaning.
Could with the Perfect Infinitive has almost the same meaning as can with the Perfect Infinitive, only the negation is not so categorical as with can.
If the action refers to the past, the Perfect Infinitive is mostly used. Other forms of the Infinitive are hardly ever used.
Note. The Russian negative-interrogative sentences of the type «Неужели она этого не видела?» are rendered in English by complex sentences:
Can it be that she has not seen it?
4. Permission.
Except in formal writing can is more common than may to express permission:
Can I use your car?
You can go now.
Can is also used to express permission for the future:
You can borrow my car tomorrow.
§ 3. May.
The verb may has two forms: may for the Present Tense and might for the Past Tense. The expressions to be allowed and to be permitted, which have the same meaning, can be used to supply the missing forms of the verb may.
"May I come along?" asked Karen. (Heym)
Jolyon thought he might not have the chance of
saying it after. (Galsworthy)
You are to stay in bed until you are allowed to get up. (Du Maurier)
May expresses permission, uncertainty, possibility, reproach.
1. Permission.