Must / Mustn't / Needn't

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Must is used to express obligation to do something in the present or the future. Have to is used in all other tenses:

Must I go? Yes, you must (go). You must not (mustn't) stay here.
Did you have to work late yesterday? 

  Must and have to can be used to express obligation in the present. But there is a difference. When must is used, it is suggested that the speaker is exercising his authority:
Jeremy is talking to his secretary and says:

You must finish this report today. (Jeremy is exercising his authority over his
secretary.)

John is copying and his classmate whispers:

You have to stop copying, the teacher is looking in this direction. (His classmate is reminding him of what is advisable to do. He has no authority over him.)

  Mustn´t  is used to express prohibition. It does not express absence of obligation. Have to in the negative form or needn´t are used to express absence of obligation:

Teacher: You mustn´t open your books during the exam. (If you open your book, you are doing something wrong / something forbidden.)
Teacher: You don´t have to bring your books tomorrow. We are going to watch a video. (If you take your books to school, you will do something unnecessary. But not something wrong.)

  Have to  is used to express obligation in all tenses:

Will you have to get up early on Sunday?
Have you had to work hard? 

  have to needs the  auxiliary verb do in questions and negative sentences:
 
 Do you have to study today? No, I don't (have to study today.)


Needn´t is used to express absence of obligation:

Teacher: You needn´t bring your books tomorrow.

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