I know him.
I don’t know him. (NOT I know not him.)
She cheated me.
She did not cheat me. (NOT She cheated not me.)
They invited us.
They did not invite us.

You will have noticed that in the sentences given above the anomalous finites help to turn positive sentences into negative sentences.

Will you come? No, I won’t.
Can I do it? No, you can’t.
Should I go? No, you shouldn’t.

In the sentences given above the verbs will, can and should are anomalous. When the verb itself is an anomalous finite negatives are made by the simple addition of not or n’t.

To form questions

Questions are usually made by putting the anomalous finite before the subject of the sentence.

He is my teacher. Is he my teacher?
They have won the race. Have they won the race?
He will come. Will he come?
She should obey. Should she obey?

Note that only the anomalous finites can be put before the subject to form questions. In the case of other finites, the auxiliary do and its forms have to be used.

He fell off the ladder. Did he fall off the ladder?
She went to the market. Did she go to the market?
She likes to watch movies. Does she like to watch movies?
I want to be a writer. Do I want to be a writer?

To form negative questions

He does not like her. Does he not like her? Doesn’t he like her?
She did not mean it. Did she not mean it? Didn’t she mean it?
He did not come. Did he not come? Didn’t he come?

Note that the forms does he not, did she not etc., are very formal. In informal speech and writing the forms doesn’t he, didn’t she etc., are preferred.

To avoid repetition of principal verbs

Do you want this? Yes, I do. (= Yes, I want that.)
Can you hear me? Yes, I can. (= Yes, I can hear you.)
Who broke my window? John did. (= John broke the window.)

To form the tag question

It is hot today, isn’t it?
She didn’t come, did she?
She can sing very well, can’t she?
They shouldn’t wait, should they?

You will have noticed that when the statement is in the positive, the tag question is in the negative and vice versa.