Use of can/am able, could/was able/may/might

Can and be able may be used in present form, can is more usual:
Sub+can/am able to+v+ob+extension.
I can do it alone.
I am able to do it alone.
He can give me money today.
We are able to punish him anytime.
I am able to cross the line easily.
He can flee away from the prison anyhow.
***Could/was able to used to mean past action.
Sub+could/was able to+v+o+extension.
I could go to the fair alone.
She was able to finish the work.
We could meet him today.
***Could  is sometimes used to mean present action:
Could you get another job? (If wanted)
***Could and was able used for past ability
When I was young like you I could/was able to run a mile at a stretch.
***Could you?  is very good way of introducing a request. It is an alternative to would you? And it shows a little polite manner.
Could you please send me an application form?
Could you lend some money?
Could you give me some money?
Could students choose what they wanted to study?
***Could or was/were allowed to for permission in the past time.
***Could can also express general permission in the past.
On Mondays we could stay at home.
On Fridays we were allowed to stay at home.
I had a visa so I was allowed to enter in the country.
Request for permission:
Can I?
Could I?
May I?
Might I?
  are all possible  and can be used for the present  or future.
Can I ? is the most informal.
Could I? is the most generally useful of the four, as it can express both formal and informal requests.
May I? is a little more formal than Could I? but can also be used for both types of requests.
Might I?  is more diffident than May I? and it indicates much uncertainty about the answer.
***May and might are used for the present and future.
***Might in the conditional and after verbs in the past tense.
If you invited him he could come.
He said that he might hire the car.
I knew we might have to wait for him there.
***May/might for present or future possibility.
Tom may lend you the money. (It stresses on may strongly but implies not very likely).
Tom might lend you the money. It stresses on might strongly  and it implies I think this  is at all likely /unlikely.
He may come today.  (Not sure)
She might help you. (But not sure)

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