Study this example:
We use must to say that we believe something is certain:
- You’ve been travelling all day. You must be tired. (travelling is tiring and you’ve been travelling all day, so you must be tired)
- ‘Joe is a hard worker.’ ‘Joe? You must be joking. He doesn’t do anything.’
- Louise must get very bored in her job. She does the same thing every day.
We use can’t to say that we believe something is not possible:
- You’ve just had lunch. You can’t be hungry already. (we don’t expect people to be hungry immediately aft er a meal)
- They haven’t lived here for very long. They can’t know many people.
The structure is:

Study this example:
Martin and Lucy expected their friends to
be at home.
They rang the doorbell twice, but
nobody has answered. Lucy says:
They must have gone out.
(= there is no other possibility)
For the past we use must have … and can’t have … :
- I lost one of my gloves. I must have dropped it somewhere. (that’s the only explanation I can think of)
- ‘We used to live very near the motorway.’ ‘Did you? It must have been noisy.’
- Sarah hasn’t contacted me. She can’t have got my message.
- Max walked into a wall. He can’t have been looking where he was going.
The structure is:

You can use couldn’t have instead of can’t have:
- Sarah couldn’t have got my message.
- Max couldn’t have been looking where he was going.