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How to distinguish use cases of these verbs?

Mustn't is a negative form of modal verb. We should use when something prohibited.

You mustn't talk in the library.

Needn't it's regular verb with negative meaning. We should use to express lack of necessity.

You needn't water the garden. Tomorrow will be rain.

Btw am I right that needn't is equal to don't have to?

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  • Yes, needn't (need not) is another way of saying don't need to, which is approximately equal to don't have to. – Kate Bunting Jan 31 at 9:25
  • 'Need vs Must' could be answered with a dictionary. The other part of your question you've answered yourself. Voting to close. – Astralbee Jan 31 at 12:07
  • @Astralbee, one more comment, please. It was not so evident to me. youtu.be/6o_BZuQ8OYk?t=35 This very popular video explains that mustn't and needn't are both modal verbs. I made this question to clarify the popular case. – dos4dev Jan 31 at 12:22
  • @Astralbee Yes, need and must are in the dictionary, but this question is specifically about the negatives, which are not in the Cambridge or Merriam-Webster dictionaries, or are only explained self-referentially. Furthermore, negatives for must and need work differently in other languages, for example German, where muss nicht means need not. – JavaLatte Jan 31 at 12:58
  • @JavaLatte This isn't a German-language site. – Astralbee Jan 31 at 17:31