Deduction

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When the speaker wants to make a deduction he uses: a modal auxiliary verb + infinitive without "to". The auxiliary verb the speaker chooses depends on the likelihood of the proposition being true. 


MUST
is used in affirmative sentences and CAN´T in negative ones when the speaker thinks that what he is saying is true or very likely to be  true

He has bought his girlfriend a very expensive diamond ring. He must have a lot of money.

He can´t have money problems.

The speaker has not been told the man in the picture is rich, he has not seen his bank account etc. but from what he has seen so far he has drawn a conclusion. He thinks he has enough information to think his conclusion is correct and he uses must in the affirmative sentence and can´t in the negative one.


MAY is used when the speaker thinks that what he is saying is perhaps true

  (It is twenty to seven. Jenny wants to phone Paul. The speaker knows Paul usually arrives home at about 7)  The speaker says: Phone him. He may be home (perhaps he is home, perhaps not).

 
MIGHT is used when the speaker thinks the chances of the proposition being true are slim (according to some grammarians).

  (Paul wants to know Jenny's phone number.) The speaker says: Ask Sally, she is not one of her close friends but she might have it.



   must, may or might + bare infinitive (infinitive without "to") are used when the deduction is about an action or situation in the present:

        
Jane always gives the right answer. She must be very intelligent.

Jim is not a very good student but he may know the answer. He likes history.


   must, may or might + continuous infinitive (be +  V-ing) are used  when the deduction is about an action or situation in progress at the time you are speaking:

        
(Sally´s coat is wet.) It must be raining.


   must, may, might + perfect infinitive (have + past participle) are used when the deduction is about an action or situation in the past.

(Jane is smiling.) She must have passed her exam.


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