Not necessarily, Nona - it's pretty hard to say which is actually the negation of (a)"you must go to the store," but certainly (b) "you must not go to the store" has a very different meaning from (c) "You needn't go to the store," (or "You don't have to go to the store.") In practice, I think (c) is more often the "opposite" or "negation" of (a) that (b) is. For instance:
Looking at it all again it is clear that must not is not necessarily the negation of must. It will depend on the degree of compulsion required. Must not is effectively banning someone from doing something.
You must not look directly at the sun during an eclipse or you will damage your eyes. No room for negotiation/personal choice here, so 'must not'.
2a] I had to go to the gym yesterday. The above is fine. What is the negation here?
2b] I hadn't go to the gym yesterday.
You wouldn't write the '2b' sentence, would you? You touched on the subject of strong nature when using the word 'must'. I would agree with you. I am still interested in the negation form of my '2a' sentence. Of course
Is that a correct use of the negation of must? Or does that explicitly mean that he has to be dragged out of the house because he is not allowed in there? (ignoring the second portion of the sentence).