Must can be used to express the conclusion that something is certain or highly probable.
- If A is older than B, and B is older is than C, then A must be older than C.
- She must have a problem – she looks worried.
- There is the doorbell. It must be your Dad.
To express certainty in questions, we usually use can. Note that must is not used in questions with this meaning.
- There is the doorbell. Who can it be?
Cannot can be used in negative clauses to say that something is certainly not the case.
- It can’t be the postman at the door. He has already been.
Need not can be used to say that something is not necessarily so. Must not is not used to express this meaning.
- ‘Look at those tracks. That must be a fox.’ ‘It needn’t necessarily be – it could be a dog.’
The structure must have + past participle is used to express conclusions about the past.
- ‘Somebody phoned while you were sleeping.’ ‘That must have been Peter.’
- She must have reached home by now.