Hello, "have to" usually expresses an obligation from the outside, eg rules, law etc... whereas "must" expresses a "personnal" obligation. " 1)a) is stronger than 1)b), which means that, all considered, something is wrong.
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Final observation: The recommendations above are based on American English, but I would not be surprised if they were valid for all other varieties of English as well. In everyday conversation in American English, the "M"-modals (may, might, must) are almost exclusively the ones used for logical deductions and similar matters. "have to", "should", and "can" are more used for strong ob