Expressing lack of necessity : do not, have to Expressing prohibition: must not

(a) I finished all of my homework this afternoon. I don’t have to study tonight.
(b) Tomorrow is a holiday. Mary doesn’t have to go to class
Don’t/doesn’t have to expresses the idea that something is not necessary
(c) Children, you must not play with matches!
(d) We must not use that door. The sign says Private: Do Not Enter
Must not expresses prohibition (Do Not Do This)
(e) You mustn’t play with matches
Must + not=mustn’t. (Note: the first “t” is not pronounced)

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Expressing necessity: have to, have got to, must

(a) I have a very important test tomorrow. I (have to/have got to/must) study tonight
Have to, have got to, and must have basically the same meaning. They express the idea that something is necessary.
(b) I’d like to go with you to the movie this evening, but I can’t. I have to go to a meeting.
(c) Bye now! I’ve get to go. My wife’s waiting for me. I’ll call you later.
(d) All passengers must present their passport at customs upon arrival.
Have to is used much more frequently in everyday speech and writing then must.
Have got to is typically used in informal conversation, as in (c).
Must is typically found in written instructions, as in (d). It is usually a strong, serious, “no nonsense” word.
(e) Do we have to bring pencils to the test?
(f) Why did he have to leave so early?
Questions: Have to is usually used in question, not must or have got to. Forms of do are used with have to in questions.
(g) I had to study last night
The Past form of have to, have got to, and must (meaning necessity) is had to
(h) I have to (“hafta”) go to downtown today
(i) Rita has to (“hasta”) go to the bank
(j) I’ve got to (“gotta”) study tonight

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Expressing advice : had better

(a) My clothes are dirty. I (should/ought to/had better) wash them
(b) You’re driving too past! You’d better slow down.
Had better has the same basic meaning as should and ought to:”This is a good idea. This is good advice.”
Had better usually implies a warning about possible bad and consequences. In (b): If you don’t slow down, there could be a bad result. You could get a speeding ticket or have an accident.
(c) You’d better not eat that meat. It looks spoiled.
Negative: had better not
(d) I’d better send my boss an e-mail right now.
In speaking, had is usually contracted:’d

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