Use Of 'Can' ,'Could', 'Could be', 'Could have' in English

Use Of 'Can' and 'Could'

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Possibility and impossibility

Can

We use can to make common statements about what is possible:

It can be very hot here in summer. (= It is sometimes very hot here in summer.)

He can be true this time.(=He often tell a lie to others.)

One can easily get lost in this large town. (= People often get lost in this town.)

He can be responsible person this time.(=He doesn’t take responsibility.)

Can’t

 We use can't or cannot to say that something is impossible:

This can't be false.
You cannot be irresponsible.

He cannot be neglected.

Could

We use could to show that something is possible, but not definite:

They could come by 9:00pm. (= Maybe they will come by 9:00pm.)
He could be at office. (= Maybe he is at office.)

Could have

We use could have to make guesses about the Past (what went before):

It's nine o'clock. They could have arrived by now.
Why are they unhappy? They could have lost today’s game.

We use could to make general statements about the past:

It could be very hot here in summer. (= It is sometimes very hot here in summer.)

He could be true that time.(=He often tell a lie to others.)

We use can't have or couldn't have to say that a past event(what went before): was impossible:

He knows the way to my office, He can't have got lost!
If James was at office until five, He couldn't have gone for the movie.

Ability

We use can and can't to speak about someone's capacity or  abilities:

He can speak several languages.
She can swim in this pond.
They can't perform very well.

We use can and can't to speak about the ability to do something at an exact time in the present or future:

I can see you.                  
Help! I can't lift this alone.

We use could and couldn't to talk about the past:

She could invite her all relatives.
They couldn't perform very well.

We use could have to say that someone had the ability or chance to do something, but did not do it:

She could have learned English language, but she didn't practice.
I could have practiced all day. [but I didn't]

Permission

We use can to ask for permission to do something:

Can I ask a question, please?
Can I go office now?

Could is more formal and polite than can:

Could I ask a question please?
Could I go office now?

We use can to give permission:

You can go home now.
You can use my laptop if you like.

We use can to say that someone has authorization to do something:

He can meet me whenever he wants.
Students can write to principal.

We use can't to refuse authorization or say that someone does not have authorization:

You can't go home before six.
Students can't play during school time.

Requests                            

We use could you … as a polite way of asking someone to do something:

Could you pass a message, please?
Could I have my mobile, please?

Can is less polite:

Can you pass a message, please?

Offers

We use can I … to make offers:

Can I help you in writing an application?
Can I do that for you?

We sometimes say I can ... or I could ... to make an offer:

I can help in that for you if you like.
I could give you my laptop to complete the assignment.

Suggestions

We use could to make suggestions:

We could meet at the weekend party.
You could go out tomorrow.

Questions and negatives

We make questions by putting the subject after can/could:

Can I...? Could I...? etc.

Can you...? Could you...?

The negative form of

      I.        can is can't in spoken English and 

   II.        Cannot in written English.

 The negative form of:

    I.        could is couldn't in spoken English and 

  II.        Could not in written English.