Deduction about the present

ModalCertaintyExample
must + infinitive Almost certain (positive) It must be cold — he's wearing a coat.
She must love books — she has a huge library.
should + infinitive Expectation / less certain He should be home by now — his flight landed at 5.
could / might / may + infinitive Possible (50% or less) It might rain later — look at those clouds.
She could be in a meeting.
can't + infinitive Almost certain (negative) — near impossible That can't be Tom — Tom is in Australia.
It can't be a burglar — all the doors are locked.
must vs can't: These are opposites. Use must when you are almost certain something is true: "You must be tired." Use can't when you are almost certain something is impossible: "You can't be hungry — you just ate!"

Deduction about the past

To make a deduction about something that already happened, add have + past participle after the modal.

ModalCertaintyExample
must have + pp Almost certain (positive) Susie is so late! She must have missed the train.
Her husband must have bought those flowers.
might/may/could have + pp Possible She might have left her keys at the office.
can't have + pp Almost certain (negative) He can't have eaten all of that — it was a huge pizza!
There's rubbish all over my garden! A fox must have been in the bin.
The kitchen was spotless. Lily must have tidied it before she went to bed.

Certainty scale

PositiveNegativeLevel
must be / must have donecan't be / can't have done95% certain
should beshouldn't be~80% (expectation)
may be / might be / could bemight not be / may not be~50% (possibility)

Exercises

must + infinitive OR must + have + past participle?

1. Keiko always does really well on exams. She ___ (study) a lot.

2. Susie is so late! She ___ (miss) the train.

3. Where is my purse? I saw it earlier, so it ___ (be) in this room.

4. There were flowers on the table when she got home. Her husband ___ (buy) them.

5. Oh no, I don't have my keys! I ___ (leave) them in the taxi.

6. If you haven't eaten all day, you ___ (be) hungry.