Page 366 - Practical English Usage 3ed - Michael Swan, Oxford

must (2): deduction (concluding that something is certain) 359 You must be Anna's sister - you look just like her.
You really must get your hair cut.
For differences between must and have (got) to, see 36l. For the difference between mllSt and SllOllld, see 520.
359 must (2): deduction
(concluding that something is certain)
1 statements: Mary must have a problem
Must can be used to express the deduction or conclusion that something is certain or highly probable: it is normal or logical, there are excellent reasons for believing it, or it is the only possible explanation for what is happening.
IfA is bigger than B, and B is bigger than C, then A must be bigger than C. I'm in love. - You must be very happy.
Mary must have a problem - she keeps crying.
There's the doorbell. It must be Roger.
2 negatives: It can't be the postman
Must is not often used to express certainty in negative clauses. We normally use cannot/can't to say that something is certainly not the case, because it is logically or practically impossible, or extremely improbable.
IfA is bigger than B, and B is bigger than C, then C can't be bigger than A. It can't be the postman at the door. It's only seven o'clock. (NOT :T mtt3tn't be
the I'BStmall ...)
She's not answering the phone. She can't be at home.
However, mustn't is used in question tags (see 487-488) after must. It must be nice to be a cat, mustn't it? (NOT ••• M lt't it?)
And must not is occasionally used, especially in American English, to say that there is evidence that something is not the case (see 361.4)
3 neednot/doesnothaveto
Need not / needn't is used (especially in British English) to say that something is not necessarily so; does not have to can also be used. Must not is not used in this sense.
Look at those tracks. That must be a dog. - It needn't be - it could be a fox. (OR ••• It doesn't have to be ...) (NOT •.• It fIltt3ffl't be ...)
4 That must have been nice
We can use must have + past participle to express certainty about the past. We went to Rome last month. - That must have been nice.
A woman phoned while you were out. - It must have been Kate. Can is used in questions and negatives.
Where can John have put the matches? He can't have thrown them away.
5 indirect speech
Must can be used after a past reporting verb as if it were a past tense. I felt there must be something wrong.
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