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The English modal auxiliary verbs are a subset of the English auxiliary verbs used mostly to express modality, properties such as possibility and obligation. [a] They can most easily be distinguished from other verbs by their defectiveness (they do not have participles or plain forms [b]) and by their lack of the ending ‑(e)s for the third-person singular.
The 'must' in this sentence thus expresses epistemic modality: "'for all we know', Agatha must be the murderer", where 'for all we know' is relative to some knowledge the speakers possess. In contrast, (2) might be spoken by someone who has decided that, according to some standard of conduct, Agatha has committed a vile crime, and therefore the ...
must: It must be hot outside. Sam must go to school. – shall: This shall not be viewed kindly. You shall not pass. – should: That should be surprising. You should stop that. – will: She will try to lie. – – would: Nothing would accomplish that. – – ought That ought to be correct. You ought to be kind.
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Last summer we would go fishing a lot. (i.e., we used to go fishing a lot) In particular, would and should are used as the past equivalents of will and shall in indirect speech reported in the past tense: The ladder will fall. → He said that the ladder would fall. You shall obey me! → He said that I should obey him.
That is, the two statements must be either simultaneously true, or simultaneously false. [4] [5] [6] In ordinary English (also natural language) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a man is a necessary condition for being a brother, but it is not sufficient ...