1. I am a good cook, amn't I?

2. I am a good cook, aren't I?
3. I am a good cook, ain't I?
4. I am a good cook, am I not?
(Which one is commonly used? Which one is used in written forms?)
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5. I amn't a good cook.
6. I aren't a good cook.
7. I ain't a good cook.
(Are the three all incorrect? Which contracted form can we use?)
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8. Amn't I a good cook?
9. Aren't I a good cook?
10. Ain't I a good cook?
11. Am I not a good cook?
(Which one is grammatically correct? Which one is correct in written forms?)

1-4 -- only 4 is correct, although the others are used by some people.

5 - 7 -- all are wrong.
The correct way to say this is
I'm not a good cook.

8 - 11 -- only 11 is correct.

1. I am a good cook, amn't I?

2. I am a good cook, aren't I?
3. I am a good cook, ain't I?
4. I am a good cook, am I not?

Out of these four options, the most commonly used and accepted version is number 2: "I am a good cook, aren't I?" This is the standard form used in spoken and written English. The other forms, while grammatically correct to some extent, may sound less natural or informal.

Regarding the second set of sentences:

5. I amn't a good cook.
6. I aren't a good cook.
7. I ain't a good cook.

All three of these sentences are technically incorrect in standard English usage. The correct contracted form in this case would be "I'm not a good cook."

Lastly:

8. Amn't I a good cook?
9. Aren't I a good cook?
10. Ain't I a good cook?
11. Am I not a good cook?

Out of these options, numbers 8 and 9 are grammatically correct and can be used interchangeably. They are both correct in written forms as well. Number 11, "Am I not a good cook?" is also correct, but it sounds more formal or old-fashioned compared to the other two options. Option 10, "Ain't I a good cook?" is still considered incorrect in standard English usage, although it may be used in informal or colloquial speech.

1. "I am a good cook, amn't I?"

This question form is grammatically incorrect. The contraction "amn't" is not commonly used in modern English and is considered archaic.

2. "I am a good cook, aren't I?"

This question form is grammatically correct. The contraction "aren't" is commonly used in spoken English to form questions. It is also acceptable to use in written forms.

3. "I am a good cook, ain't I?"

This question form is grammatically incorrect. "Ain't" is a non-standard contraction and is considered informal. It is generally discouraged to use "ain't" in formal or written English.

4. "I am a good cook, am I not?"

This question form is grammatically correct. It is a formal and more precise way to ask a question, commonly used in written forms.

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5. "I amn't a good cook."

This statement is grammatically incorrect. The contraction "amn't" is not commonly used in modern English and is considered archaic. The correct form is "I am not a good cook."

6. "I aren't a good cook."

This statement is grammatically incorrect. The correct form is "I am not a good cook." The contraction "aren't" is used with "you," "we," "they," and "those," not with "I."

7. "I ain't a good cook."

This statement is grammatically incorrect. "Ain't" is a non-standard contraction and is considered informal. The correct form is "I am not a good cook."

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8. "Amn't I a good cook?"

This question form is grammatically incorrect. The contraction "amn't" is not commonly used in modern English and is considered archaic. The correct form is "Aren't I a good cook?"

9. "Aren't I a good cook?"

This question form is grammatically correct. The contraction "aren't" is commonly used in spoken English to form questions. It is also acceptable to use in written forms.

10. "Ain't I a good cook?"

This question form is grammatically incorrect. "Ain't" is a non-standard contraction and is considered informal. The correct form is "Aren't I a good cook?"

11. "Am I not a good cook?"

This question form is grammatically correct. It is a formal and more precise way to ask a question, commonly used in written forms.