Auxiliary verbs

In each of these sentences there is an auxiliary verb and a main verb:

In these examples have/can't/was/do are auxiliary (= helping) verbs.

• 'Have you locked the door?'  'Yes, I have.' (= I have locked the door)
• Gary wasn't working, but Laura was. (= Laura was working)
• Jessica could lend me the money, but she won't. (= she won't lend me the money)

• 'Do you like onions?'  'Yes, I do.' (= I like onions)
• 'Does Simon live in London?'  'He did, but he doesn't any more.'

• 'You're sitting in my place.'  'No, I'm not.' (= I'm not sitting in your place)
• 'You didn't lock the door before you left.'  'Yes, I did.' (= I locked the door)

We use have you? / isn't she? / do they? etc. to show interest in what somebody has said, or to show surprise:

• 'I've just seen Stephen.'  'Oh, have you? How is he?'
• 'Lisa isn't very well today.'  'Oh, isn't she? What's wrong with her?'
• 'It rained every day during our holiday.'  'Did it? What a shame!'
• 'James and Tanya are getting married.'  'Are they? Really?'

We use have you? / isn't she? / do they? etc. to show interest in what somebody has said, or to show surprise:

• 'I've just seen Stephen.'  'Oh, have you? How is he?'
• 'Lisa isn't very well today.'  'Oh, isn't she? What's wrong with her?'
• 'It rained every day during our holiday.'  'Did it? What a shame!'
• 'James and Tanya are getting married.'  'Are they? Really?'

I think so / I hope so etc.

• 'Are those people Korean?'  'I think so.' (= I think they are Korean)
• 'Will you be at home this evening?'  'I expect so. (= I expect I'll beat home ... )
• 'Do you think Kate has been invited to the party?'  'I suppose so.'

In the same way we say: I hope so, I guess so and I'm afraid so.

The usual negative forms are:

• 'Is that woman American?'  'I think so. / I don't think so.'
• 'Do you think it will rain ?'  'I hope so. / I hope not.' (not I don't hope so)