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

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

3. I aren't a good cook.
4. I ain't a good cook.
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Are they possible to use?

None of those is standard English, although 2 is often used.

I'm a good cook, am I not?
I'm not a good cook.

1. The correct form of the sentence would be: "I am a good cook, aren't I?" This is the grammatically correct way to express the question. "Ain't I?" is a colloquial or informal form that is generally considered non-standard English.

2. The correct form of the sentence would be: "I am a good cook, aren't I?" This is the grammatically correct way to express the question. "Ain't I?" is a colloquial or informal form that is generally considered non-standard English.

3. The sentence "I aren't a good cook" is not grammatically correct. The correct form would be "I am not a good cook." "Aren't" is the contraction of "are not," and it cannot be used with the pronoun "I."

4. The sentence "I ain't a good cook" is a colloquial or informal form of "I am not a good cook." While "ain't" is not considered standard English, it is commonly used in spoken language, particularly in certain dialects or informal settings. However, in more formal or written communication, it is generally recommended to use "am not" or "are not" instead of "ain't."

1. The sentence "I am a good cook, ain't I?" is not grammatically correct. The word "ain't" is a colloquial contraction that is often used in informal speech, but it is not considered grammatically correct in standard English. In this case, the correct phrase to use would be "am I not?" So the correct version of the sentence would be "I am a good cook, am I not?"

To form a question tag in the positive form, you generally use the auxiliary verb from the main part of the sentence, followed by the personal pronoun and the appropriate form of the verb "be" (e.g., "am," "are," "is," "was," "were"). In this case, the auxiliary verb is "am," so the question tag should be "am I not?"

2. The sentence "I am a good cook, aren't I?" is grammatically correct and can be used in conversation. The word "aren't" is a contraction of "are not," and it is commonly used in informal speech to form negative question tags. So, this sentence is a proper form of using a question tag in the negative form.

3. The sentence "I aren't a good cook" is grammatically incorrect. The correct form should be "I am not a good cook." The word "aren't" is a contraction of "are not," which is used to negate the verb "be" in the present tense with the subject "you," "we," or "they." In this case, the subject is "I," so the correct contraction for negation is "am not."

4. The sentence "I ain't a good cook" is a grammatically incorrect form that is often used in informal speech or dialects. The correct form would be "I am not a good cook." The word "ain't" is a colloquial contraction of "am not," "are not," or "is not," but it is not considered standard English. So, although this sentence is commonly used in casual conversation, it is not grammatically correct in formal writing or speech.