Modal verbs: can, could, be able to

Ability
I can play piano. I play every day.
He can not play piano at all.
Can you play piano or guitar?
She could swim well in childhood.
They could not swim very well.
Could he swim well in childhood?

Usage: Modal verb ‘Can’ shows that you know how to do something and it’s possible for you to do it. ‘Could’ has the same usage but refers to the past.

Request
Can you open the door, please?
Could you open the door, please?

Usage: We use ‘Can…?’ or ‘Could…?’ when we ask people to do something. There is slightest difference ‘Can…?’ is like asking ‘Are you able to…?’ whereas ‘Could…?’ is more like ‘Are you willing to…?’ That’s why ‘Could…?’ seems more polite.

Could do & Could have done
I’m so tired I could sleep for a week.
I was so tired I could have slept for a week.
 The situation is perfect, it could not be better.
Situation was perfect, it could not have been better.
Why are you staying here? You could stay with me.
You could have stayed with me last holiday.

Usage: We use ‘could’ for actions that are not realistic, or possible now or in the future. We use ‘could have done’ to talk about past with the same aspect as ‘could’.

to be able to
‘Can’ has only 2 forms ‘can’ and ‘could’. Sometimes it’s necessary to use ‘be able to’, which has the same meaning with ‘can’.
I haven’t been able to sleep recently.
Tom might be able to come soon.
She must be able to speak Arabic.

There is small difference between ‘could’ and ‘was able to’ in positive sentences. He played well and could beat anyone. So he had general ability to win. He didn’t know how to play, but was able to beat his opponent. So he managed to win.

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