Are they cooks?

1. No, they are not.
2. No, they're not.
3. No, they aren't.
[Are the three answers grammatical?]

4. Max isn't my pet.
5. Max's not my pet.
[Is #5 grammatical?]

6. Betty and I aren't late for school.
7. Betty and I're not late for school.
[Is #7 grammatical?]

Let's see your answers first.

1-6 are fine.

7 is not.

Thank you.

4. Max isn't my pet.
5. Max's not my pet.
[Is #5 grammatical?]
5-1. Max' not my pet. [What about this one?]
How do you pronounce "Max's"?

Yes, all three answers are grammatical. In English, there are multiple ways to form negative contractions using "not" or "n't."

1. No, they are not. This is a grammatically correct answer that uses the full form of "not" without any contraction.
2. No, they're not. This is also grammatical, where "they're" is a contraction of "they are" and "not" is added to form the negative.
3. No, they aren't. This is another correct answer, using the contraction "aren't" which is a contraction of "are not."

Regarding the next set of examples:

4. Max isn't my pet. This sentence is grammatical and correctly uses the contraction "isn't" which is a contraction of "is not."

5. Max's not my pet. This sentence is also grammatical, although it uses a different contraction. "Max's" is a contraction of "Max is" and "not" is added to form the negative. While less common, this type of contraction is still acceptable in casual speech or informal writing.

Finally:

6. Betty and I aren't late for school. This sentence is grammatically correct and uses the contraction "aren't," which is a contraction of "are not."

7. Betty and I're not late for school. This sentence is not grammatically correct. While it attempts to use the contraction "I're" as a short form of "I am," this contraction is not standard in English. The correct contraction would be "I'm" (I am), so the correct sentence would be "Betty and I'm not late for school."