Use of Can/Could/be able to

Can, Could, Be Able To

Can, could and be able to are used to express a variety of ideas in English:
Ability/lack of ability
Present and future
Can/can't+ v1 (base form of verb)
Sona can sing. It means Sona has ability to sing.
Sona can't sing. It means does not know singing.
Be + able to is an alternative form of can for the present tense where be stands for is/am/are. But of two options CAN is more usual and accepted form in day to day conversation
She can run fast means she is able to run fast.
Has been/have been able to is the present perfect form of (be able to) discussed above.

The present perfect tense (sometimes also called the perfect tense) describes action that started before the time you are speaking of, but ends in the time you are speaking of. Have been is in the present perfect tense. Use it when you want to say that someone or something started an action in the past and finished it in the time being spoken of:

I have been able to visit them regularly.

(In this sentence, the speaker started visiting them sometime in the past and is still visiting them at the time being spoken of).
Example in negative
She has not been able to visit them regularly.
To express the same ability/lack of ability we use could or be able to where be stands for was/were
Example
Rohan was able to pass the examination
Or
Rohan could pass the examination

To express lack of ability we use negative adverbs
Example
Rohan could never pass the examination though he appeared in the examination four times.
Had been + able to is the past perfect of be able to and it means that the speaker could/could not do the mentioned task in the past but opposite happens now
I had been able to run one mile daily when I was youth.
I had not been able to run one mile daily when I was youth.

Could + perfect infinitive is used to express non-fulfilment in the past. Thus it is equivalent to negative simple in the past.
Mohan could have got a good job in those days. It means Mohan didn't get a good job.
Can is also used to express permission
Ex- can I go out but it appears to be rude at formal places so it is avoidable.
Cam also expresses possibility.
Can it be murder?
Can+ perfect infinitive is used to express a deduct or assumption about a past possibility.
Example: He can have caught the first train in any case.
Can't/couldn't be is used to express a negative deduction or assumption about a present action
The flying object can't/couldn't be a bird.
Could is also the most polite form of asking permission
Example
Could I talk to your supervisor, please?
Or could I have your number?

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