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'Must' indicates obligation (you have to do it); 'mustn't' indicates prohibition (you must not do it).
Side-by-side comparison
"Must" expresses a strong obligation or a positive deduction. Depending on context, it means "you have to" or "it must be true".
You must try this restaurant, the food is incredible and very affordable too.
She must be exhausted, she has been working nonstop since early this morning.
Students must show their ID card to enter the library after six in the evening.
"Mustn't" is not the negative of obligation: it does not mean "you do not have to". It means something is prohibited or you must not do it. To say something is not necessary, use "don't have to".
You mustn't touch the paintings in the museum, there are signs everywhere reminding you.
You mustn't tell her about the surprise party, it has to be a secret until Saturday.
Passengers mustn't leave their luggage unattended at any time inside the airport.
Common mistake
Mixing them at work can sound like a scolding without meaning to: "You mustn't come to the meeting" is an order not to come. If you meant that they are free to skip it, say "You don't have to come".
Trick to remember it
Three states: obligation = "must / have to". Prohibition = "mustn't / cannot". No obligation = "don't have to / don't need to". "Mustn't" = do not do this. "Don't have to" = it is your choice.
Quick rule
"Must" = obligation. "Mustn't" = prohibition (not allowed). "Don't have to" = no obligation (not necessary). "Mustn't" and "don't have to" are opposites.
Did you know?
The asymmetry between MUST (positive) and its negative equivalents is one of the most fascinating phenomena of English modal grammar. MUST in positive = obligation. MUSTN'T = prohibition (not absence of obligation). DON'T HAVE TO = absence of obligation. This means that to negate obligation in English, you must completely change the modal verb (from MUST to HAVE TO). This phenomenon is called "modal supletivism" and is common with English modals: WILL has no true past (WOULD or WAS GOING TO is used). CAN has no infinitive (BE ABLE TO is used). English modals are remnants of Proto-Germanic strong verbs that have lost many of their forms over time.
Practise what you learned
Exercise 1 · Pick the right one
You _____ wear a seatbelt in a car. It's the law in most countries.
Exercise 2 · Pick the right one
You _____ touch that wire. It's dangerous and could give you an electric shock.
Exercise 3 · Form the word
Related word pairs
"Can" expresses ability or capacity (to be able to do something); "may" expresses formal permission or possibility (something might happen).
'Have to' expresses external obligation; 'need to' expresses functional or personal necessity.
"Must" is internal obligation or logical deduction; "have to" is external obligation imposed by others.
'Must' can express obligation or deduction; 'can't' (not 'mustn't') expresses the negative deduction.
Bryan López
Founder of SpeakUP Academy