How to change negative statements with modal auxiliary verbs into negative questions

Here’s how to change negative statements with modal auxiliary verbs into negative questions, with explanations and examples using daily sentences:

1. Can (cannot → can't)
Statement: They cannot dance. 
Negative Question: Can they not dance?
Explanation:
To form a negative question, move can to the beginning, and place not after the subject (they).

With contraction:
Question (informal): Can’t they dance?

2. Could (could not → couldn't)
Statement: He could not come to the party.
Negative Question: Could he not come to the party?
Explanation:
To form the negative question, invert could and he, with not after the subject.

With contraction:
Question (informal): Couldn't he come to the party?

3. May (may not)
Statement: She may not leave early. 
Negative Question: May she not leave early?
Explanation:
For a negative question, move may to the start and keep not after the subject.

With contraction:
Question (informal): Mayn't she leave early?

4. Might (might not → mightn't)
Statement: He might not go to the park. 
Negative Question: Might he not go to the park?
Explanation:
Invert might and he, and place not after the subject to form the question.

With contraction:
Question (informal): Mightn't he go to the park?

5. Must (must not → mustn't)
Statement: We must not finish the report. 
Negative Question: Must we not finish the report?
Explanation:
To form the negative question, place must at the beginning, and not after the subject.

With contraction:
Question (informal): Mustn't we finish the report?

6. Shall (shall not → shan't)
Statement: We shall not meet tomorrow.  Negative Question: Shall we not meet tomorrow?
Explanation:
To form the negative question, move shall before we and keep not after the subject.

With contraction:
Question (informal): Shan't we meet tomorrow?

7. Should (should not → shouldn't)
Statement: He should not study harder. 
Negative Question: Should he not study harder?
Explanation:
To form the question, move should before he and keep not after the subject.

With contraction:
Question (informal): Shouldn't he study harder?

8. Will (will not → won't)
Statement: She will not join us later. 
Negative Question: Will she not join us later?
Explanation:
Move will to the front and keep not after the subject.

With contraction:
Question (informal): Won't she join us later?

9. Would (would not → wouldn't)
Statement: He would not like some coffee. Negative Question: Would he not like some coffee?
Explanation:
Invert would and he, and place not after the subject.

With contraction:
Question (informal): Wouldn't he like some coffee?

Contraction use in Negative Questions:
In informal speech, contractions are common in negative questions:

1. Can they not → Can't they?
2. Could they not → Couldn't they?
3. Must they not → Mustn't they?
4. Shall we not → Shan't we?
5. Will they not → Won't they?
6. Would they not → Wouldn't they?

Summary of the Process:

1. Identify the modal auxiliary verb in the negative statement (e.g., can, could, may, etc.).
2. Invert the modal auxiliary verb and the subject, and place not after the subject.
3. Use contractions like can't, won't, or shouldn't for a more conversational tone.