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When we talk about ability, we mean two things.
First, we mean general ability. This is something that once you have learned you can do any time you want, like being able to read or swim or speak a language, for example.
The other kind of ability is specific ability. This mean something that you can or can't do in one particular situation. For example, being able to lift something heavy, or find somewhere you are looking for.
Present:
can / can't (for both general and specific ability)- I can play the piano.
- She can speak English.
- He can't drive - he's too tired.
- We can't come now.
Past:
could / couldn't (for general ability)- I could read when I was four.
- She could speak French when she was a child, but now she has forgotten it.
- He couldn't dance at all until he took lessons.
- My grandfather couldn't swim.
- When the computer crashed yesterday, I was able to fix it.(not 'I could fix it')
- She was able to pass the exam, even though she hadn't studied much.(not 'she could pass')
- He called us because he couldn't find the house.
- I couldn't open the window.
- I could have played the piano well but I didn't practise enough.
- We could have come earlier.
- She could have studied law, but she preferred to become a secretary.
Future:
will / won't be able to (general ability)- At the end of the course, you will be able to make your own website.
- He won't be able to speak Japanese in a week! It will take months.
- I can help you tomorrow
- I can't come to the party