We use must to say that we are sure about something in the present or past
– You must be pleased with your exam results. (present)
– He must have touched up the photograph. (past)
We use can’t or couldn’t, not mustn’t, in negative sentences
– That can’t be Nicole Kidman. She’s not young enough. (present)
– They can’t have got lost. They know the area really well. (past)
– It couldn’t have been Tom that I saw. (past)
Strong obligation and necessity
We use must/mustn’t to talk about present and future obligations/prohibitions imposed by the speaker, often to him/herself
– Payment must be made in cash.
– I must get some new shoes.
– Must I really go now?
– You must read that book – it’s excellent! (=recommendation)
– You mustn’t park here. (= prohibition)
– You mustn’t eat so much (= strong advice)
We use have to/have got to to talk about present and future obligations that are imposed by someone other than the speaker
Note: have got to is more in British than American English.
– I have (got) to take my holiday in February.
– Do we have to pay to go in?
We use had to to talk about past and reported obligations of all kinds
– They told us we had to leave our bags in the cloakroom.
– We had to stand up when the teacher came in.
– I knew I had to make a decision.
We can also use need to to talk about obligation and necessity
– Do we need to type our work?