We can use modal verbs to talk about how sure or unsure we are about something in the past just as we use modals in the present with a slight change in the form.
He must be really happy about his promotion. (present deduction)
He must have been very happy when he was told about his promotion. (past deduction)
When we use a modal verb to talk about a situation where we are not expressing a fact but we are using deduction the form is MODAL + have + past participle (verb 3)
Must have + past participle
We use ‘must have + past participle’ when we are quite sure about something.
You must have been very pleased when you received the results of your exams.
He must have forgotten his phone at home again. He’s not answering.
I must have left my keys in the car. I can’t find them.
Might have/may have/could have + past participle
We use ‘might have/may have/could have + past participle’ when we are not sure about something but we think it was possible.
He was supposed to be here an hour ago but he could have been stuck in a traffic jam.
He may have said he was coming but I can’t really remember. I wasn’t listening.
I might have been here when I was a child but I can’t really remember.
Can’t have + past participle
We use ‘can’t have + past participle’ for things that we are sure did not happen in the past.
I can’t have left my phone at work. You phoned me when I was walking to my car. That’s it. It must be in the car.
You can’t have seen him this morning. He was with me all the time.
She can’t have liked the show. She hates musicals.
Lesson by Tristan, teacher at EC Malta English school
Now put the correct modal in these sentences.