We can use modal verbs for deduction – guessing if something is true using the available information. The modal verb we choose shows how certain we are about the possibility.
must have
We use must have + past participle when we feel sure about what happened.
Who told the newspapers about the prime minister's plans? It must have been someone close to him.
The thief must have had a key. The door was locked and nothing was broken.
might have / may have
We can use might have or may have + past participle when we think it's possible that something happened.
I think I might have left the air conditioning on. Please can you check?
Police think the suspect may have left the country using a fake passport.
May have is more formal than might have. Could have is also possible in this context but less common.
can't have / couldn't have
We use can't have and couldn't have + past participle when we think it's not possible that something happened.
She can't have driven there. Her car keys are still here.
I thought I saw Adnan this morning but it couldn't have been him – he's in Greece this week.
Revision
https://www.esl-lounge.com/student/grammar/4g3-modals-deduction-exercise.php
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