Must as an auxiliary verb

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To express a conclusion

Must can be used to express the conclusion that something is certain or highly possible.

Must in questions and negatives

Must is not often used to express certainty in questions and negative clauses. In questions we use can.

In negative clauses we generally use cannot/can't to say that something is certainly not the case.

However, mustn't is normal in question tags after must, and in negative questions.

To express necessity

Must is often used in affirmative sentences to say what is necessary, and to give strong advice and orders to ourselves and other people.

Must can be used in questions to ask about what the hearer thinks is necessary.

In American English, have to is more common.

Must not or mustn't is used to say that things should not be done, or tell people not to do things.

Sections in this article

Modal Auxiliary Verbs
May and Can: differences
Should: other uses
Must: uses
Must and have to: The Difference
Ought to
Had better
Should, Ought and Must: The difference