Could, Should, must

​could/may/might.

Could= possibilities besides conditional uses. could/may/might give same meaning.

It might/may/ could rain tomorrow= it will possibly rain tomorrow. Or maybe it will rain tomorrow.

Maybe(combination of  may+be but not an auxiliary and means perhaps)

The leader said there might be a strike next week. I may go to the beach or I may stay home. It might be warmer tomorrow. I may not be able to go with you tonight. John could be at home(I don’t know where sima exactly is) .

should.

Recommendation, advice, obligation.

She should study tonight.

Sima should go on a diet.

You should visit a dentist about this teeth problem.

Should= had better, ought to, be supposed to.

Sima should (had better/ought to/is supposed to) go on a diet.

must 

To indicate complete obligation, stronger than should.( no choice left as in should).

You must endorse a check before you cash in.

She must call her insurance agent today.

The freezer must be kept at -20 degrees.

For logical conclusion , too, must is used.

The leaves are rustling. There  must be air flow. 

The grass is wet. It must be rainin

 have to.

Have to=must.

She has to call her insurance agent today.

For past obligation, must doesn’t have any words so had to is used.

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