Must and can't

A. Study this example:

 You can use must to say that you believe something is certain:

• You’ve been travelling all day. You must be tired. (Travelling is tiring and you’ve been travelling alt 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.
•  I’m sure Sally gave me her address. I must have it somewhere.

You can use can’t to say that you believe something is not possible:

• You’ve just had lunch. You can’t be hungry already. (People are not normally hungry just after eating a meal. You’ve just eaten, so you can’t be hungry.) 
•  They haven’t lived here for very long. They can’t know many people.

Study the structure:

B.  For the past we use must have (done) and can't have (done).

•  ‘We used to Live very near the motorway.’ 'Did you? It must have been noisy.’ 
•  ‘I’ve lost one of my gloves.’ 'You must have dropped it somewhere.’
•  Sarah hasn’t contacted me. She can’t have got my message.
•  Tom walked into a waLl. He can’t have been looking where he was going. 

Study the structure:

You can use couldn’t have instead of can’t have:

• Sarah couldn’t have got my message. 
•  Tom couldn’t have been looking where he was going.