Hey Katherine, I shall provide you an explanation over the usage of ''can't have...'' and ''couldn't have...'': *First of all, you should know that ''can't have'' and ''couldn't have'' share a similar degree of probability. They are equal in meaning when they express the impossibility of something. 1) "Can't have..." suggests that it happened more recently. It expresses a judgment about a recent action or situation, a context in which the issues are still fresh and relevant to the present. E.g.: ''Can you check my homework? I'm quite sure I can't have found every bug.'' 2) "Couldn't have" suggests that it was further in the past. E.g.: ''As a young woman who had never given birth before, she couldn't have known what the experience of childbirth would be like.'' ***NOTICE: ''Can't have'' is used to express negative obligation or permission, while ''couldn't have'' carries no such meaning. This use of ''can't have'' means "You are not allowed to have (done something...)." E.g.: ''You have to write it during the class, you can't have written it beforehand.'' As to your question, I should say that, although ''can't have'' is used much less than ''couldn't have'' in normal conversation, the expression ''can't have...'' expresses an idea of assurance about something the person regards as true. Hope that helps!

I am not an English speaker at all , but the answer he can not have sent you this letter is correct, because there's a lot of assurance in the first sentence ... and there's no assurance in the form could have sent... Could have sent or could not have sent this is a question. He can't have sent you this letter means,. I am almost a hundred percent sure he did not do that. I do not know how much helpful my explanation is though

1) Could is the past of can, right? So, if that phrase was in the past, its correct because you will talking about an ability in the past. But It is present, so you need use can.

xx

2) Its the same case of the firts one.