Can and be able to are both used to talk about ability. Sometimes they’re interchangeable, but sometimes they’re not. So, let’s start by looking at your examples. You’ve asked about can’t and unable to. Well, we use can’t in the present tense when we say that we don’t have the ability to do something — for example, I can’t swim.

We could also say I am unable to swim, and the meaning would be pretty much the same. But which one do we choose? Well, for informal English, and for spoken English in particular, people tend to use can or can’t. Able to seems a bit more formal and not really appropriate for everyday situations.

Now the past of can is could, and the past of be able to is was able to or were able to. For example, we can say:

I could swim (or I couldn’t swim ) when I was 7 years old

or we can say

I was able to swim (or I was unable to swim ) when I was 7 years old

Again, in spoken English, we’d probably use could or couldn’t to talk about past ability or lack of ability. Now the examples I’ve just given are concerned with general ability.

I could swim when I was 5 years old

It refers to a general ability, not an ability in a specific past incident. It’s important to understand this difference because when we talk about ability in specific past incidents, the way we use could and was able to changes. I’ll tell you a story as an example.

When I was 10 years old, my mother and father took me on a sailing holiday, and on the last day, when the sea was very rough, I fell out of the boat! It was OK though, I was able to swim back to the boat.

I was able to swim back to the boat.

It’s describing an ability in a specific past event, and we would NOT normally say

I could swim back to the boat.

But what about the negative form? Well, on the same trip, my younger sister fell into the water too. But she wasn’t a strong swimmer, and my father had to jump into the sea and rescue her, because she couldn’t swim back to the boat. So to talk about lack of ability in a specific past event, couldn’t is OK. We could also say:

She wasn’t able to swim back to the boat or

She was unable to swim back to the boat.

OK? Now I’m going to deal with future, present perfect and past perfect tenses, by telling you that can is not normally used to describe ability in these tenses. For these tenses, you have to use be able to or be unable to. Here are some examples and don’t forget that when you use unable to, it gives a more formal tone than not able to. Here’s an example in the future:

You’ll be able to speak really good English by the end of the year. And now one in present perfect:

We’ve been unable to complete the project within the specified budget.

The next one is present perfect, question form:

How long has your little boy been able to read?

And let’s listen to a past perfect — this one’s negative:

He was given a detention because he hadn’t been able to finish his homework.

Now, although we’ve just said that we don’t usually use can or can’t to talk about future ability, it is possible to use can to suggest a possible future action, like this:

I can join you at the meeting, but I can’t stay very long.

	Positive	Negative structure / meaning	Question
Present	I can workI am able to work	I can’t workI am not able to work I am unable to work	Can I work?Am I (un)able to work?
Past	I could workI was able to work	I couldn’t workI was not able to work I was unable to work	Could I work?Was I (un)able to work?
Future	I will / shall be able to work	I won’t / shan’t be able to workI will / shall be unable to work	Will / shall I be (un)able to work?
Present perfect	I have been able to work	I haven’t been able to workI have been unable to work	Have I been (un)able to work?
Past perfect	I had been able to work	I hadn’t been able to workI had been unable to work	Had I been (un)able to work?

В каком случае правильно говорить «big», а в каком «large»?

Well, this is a big question Iryna, so I’ll do my best to answer it clearly and briefly!

First I’ll talk about form: ‘Large’ and ‘big’ are both regular adjectives… their comparative forms are ‘larger’ and ‘bigger’; their superlative forms are ‘largest’ and ‘biggest’. ‘Big’ is a very common word in both written and spoken English; in fact, it’s in the top 1,000 most frequently used words.

‘Large’, on the other hand, is a less frequently used word and doesn’t even make it into the top 3,000 most frequently used words in English. Now, onto the question of meaning… The general meaning of both ‘large’ and ‘big’ is: ‘of more than average size/amount/weight/height’ etc. For example:

‘Iryna has got a well-paid job and can afford to live in a house’ — OR…  ‘Iryna lives in a large house’.

In these examples, both ‘big’ and ‘large’ mean that Iryna’s house is of more than average size. Although ‘big’ and ‘large’ both mean the same in these examples, ‘large’ sounds a little more formal.  Neither ‘large’ nor ‘big’ can be used with uncountable nouns.  This means, we can say:

‘The house has a (big or large) garden’ — because ‘garden’ is countable. However, we can’t use ‘big’ or ‘larg’ with ‘traffic’, because ‘traffic’ is uncountable.  With uncountable nouns, you can use ‘a lot of’ — for example:

‘There’s a lot of traffic on the road next to the house.’

So, although ‘large’ and ‘big’ are often interchangeable, sometimes they are not.  So next, I’ll try and give you some examples of when this is the case… ‘Big’ can mean ‘important’, for example:

‘Buying a house is a very big decision’.

It can also be used in informal situations to mean ‘older’, for example:

‘He’s my big brother’… as well as ‘successful’ or ‘powerful’, for example: ‘York is a big tourist destination’.

Also in informal situations, we can use ‘big’ to mean ‘doing something to a large degree’, for example: 

‘She earns a lot of money, but she’s also a big spender’ — OR… ‘I’m a big fan of yours’. ‘Big’ is used in a lot of fixed phrases, and because these phrases are fixed, to change ‘big ‘to ‘large’ would sound wrong. Examples of fixed phrases using ‘big’ include:

‘It’s no big deal’ — it’s not really important.
‘I have big ideas for this house’ — impressive plans for the future.
‘She’s a big mouth’ — a person who can’t be trusted to keep a secret.
‘He’s too big for his boots’ — too proud of himself.

There are also some fixed phrases using ‘large’. Examples include:

‘The prisoners are at large’ — they have escaped and may cause harm. 

‘She’s larger than life’ — more exciting or amusing than most people.

Finally, quantity words…. ‘large’, more often than ‘big’, is used with the following quantity words:

‘a large amount’, ‘on a large scale’, ‘a large number of’, ‘a large quantity of’, ‘a large proportion’, ‘to a large extent’, ‘a large percentage of’, ‘a large part of’, ‘a large volume’ and ‘a large area’. So……a very big — or large — question, Iryna! I hope this has helped a little!