Meaning of negation in embedded yes/no interrogatives

Solution 1:

The basic form of the direct question would be

"Don't you like beer?"

and, while

"You don't like beer, do you?"

is semantically identical, we use it in a different context. The first question is one of surprise (if she seems not to) or affirmation (if you believe she does). The second question is looking for confirmation of your belief that the other person doesn't like beer, either personally or because you feel beer is just awful and all right-thinking people avoid it.

Pace @MaddieS. you should never answer a negative question with a one-word answer. It's completely ambiguous whether that means you're negating the question or affirming it. You'll spend the next minute or two of the conversation in needless loop trying to figure out what was intended, which can be offputting when someone expects their logic or phrasing should have been straightforward. Instead, just answer the whole thing: "No, I don't", or "Yes, I don't like beer at all".

Solution 2:

Negation in yes/no questions makes no difference to their essential meaning. The answer to a yes/no question and the answer to it's negated version will be the same:

• Do you like beer? No, I don't
• Don't you like beer? No, I don't

The main difference between a normal question and a negated one is that the negation tends to imply a previous bias on the part of the speaker towards an affirmative answer. You will notice that the question "Don't you like beer" seems to imply that the speaker thought that they did like beer, and is surprised that they don't.

This implied bias is often cancelled if the question seems to be prompted by some kind of contextual evidence. Usually, in these kinds of question the word not is not attached to the auxiliary:

• Mary doesn't drink beer.
• Do you not drink beer either?

In the question above, the speaker does not seem to imply that they had a strong impression that the other person did drink beer. Here, the bias - if there is any - seems to be that the speaker suspects that the other person may not drink beer. Notice that if we stick the negative onto the auxiliary the bias will be reintroduced:

• Mary doesn't drink beer.
• Don't you drink beer either?

We can easily embed both of these types of negative question in reported speech. However, without any context such questions will seem to lose their implied bias. One of the reasons for this is that in reported speech it doesn't make much difference whether we use the word not or a negative contraction. So in the sentence -

• I asked him if he didn't like beer.

We don't necessarily get a strong sense of affirmative bias even though the the negation is attached to the auxiliary. So the original question could easily be either of the following:

• Do you not like beer?
• Don't you like beer?

The fist of these may or may not imply any bias, depending of the context.