1. Does Tom like pears?

2. No, he doesn't.
3. No, Tom doesn't.

4. Doesn't David like roses?
5. No, he doesn't.
6. No, David doesn't.
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Do you mean all the answers are grammatical? Can we use #3 and #6?

1 answer

All the answers are fine, yes.

#s 2 and 5 are best, but #s 3 and 6 work, too.