Let's say I have two daughters and someone asks me:
Do you have a daughter?
Should I respond "yes" or "no"? In other words, does "I have a daughter" mean "I have one daughter"?
"I have a/an X" does not necessarily mean that I have exactly one X, it just means that I have one or more.
Suppose someone was looking for a ride home, and he asked, "Do you have a car?" If you own two cars, you wouldn't say, "No". You probably wouldn't even find it necessary to say, "I have two cars". You'd just say "Yes". (Well, unless you're looking for an excuse to not give him a ride.)
Suppose your local school announced they were having a "father/daughter dance", and said, "This is open to any man who has a daughter in this school." If you have two daughters, would you conclude that you were not welcome? Almost certainly not.
Or to take it a step further, if someone asked, "Do you have a daughter?", and in fact you have one daughter and one son, would you say, "No, I don't?" Probably not. Or if someone asked, "Do you own a cell phone?", would you say "no" because you own a cell phone and you own a laptop computer and you own a car and you own six pairs of underwear, etc? Normally, asking if you "have X" doesn't imply "and nothing else". If you want to specify "and nothing else", you normally need to add some words, like "only" or "just one". Like if someone asked me, "Do you have only one daughter?", I would answer, "No, I have two." I might also say that I have two sons as well, if the context of the question implied that the person was asking if I had only daughters.
All that said, there may be contexts where it would be understood to mean exactly one. I can't think of one, but I can think of a somewhat similar example. Suppose someone said, "In this country it is illegal for anyone under 18 to buy alcohol." If in fact the law said it is illegal for anyone under 21 to buy alcohol, there's a sense in which the statement is technically accurate: Yes, it is illegal for anyone under 18 to buy alcohol. But it is also illegal for anyone between 18 and 21 to buy alcohol. But as worded the sentence is very misleading. It implies that anyone over 18 can buy alcohol, without actually saying that.
I suppose if someone said, "We are holding a conference for parents of girls being raised without any brother or sisters, only children who are girls. You sir, do you have a daughter?" Clearly then he means exactly one, but this example is highly contrived.
You asked about answering "yes" or "no". If the question is "do you have a daughter" and you have one, two or more daughters, then the correct answer is "yes".
However, if I ask the question, I might get the answer "yes, I have a daughter" and the problem is: Does the person have exactly one daughter or possibly more than one?
It depends on the context. Let's say I have trouble with my daughter and some know-it-all is trying to give me advice, which really gets on my nerves. So I ask "do you have a daughter?" because that kind of unwanted advice often comes from people who know nothing. In that case an answer "yes, I have a daughter" means one or more daughters. My question really meant "do you know what you are talking about" and the answer meant "yes, I know what I'm talking about".
In other situations, you would expect "I have a daughter" to mean "I have one daughter", and you would expect a different answer like "I have two daughters" from someone with more than one daughter. Then of course it depends on how much of a pedant the person is, so your expectation might be wrong.
The long standing play on words relating to this subject is this joke:
"Hey, you got a haircut!" "Actually, I got all of them cut!"
This is funny (or supposed to be funny) exactly because "a haircut" (the act of getting your hair cut) sounds exactly like "a hair cut" (you got exactly one of your hairs cut), and the deliberate misinterpretation is unexpected.
The fact that this answer is unexpected highlights how strange it would be to me to answer anything other than "Yes" to the original questioner.
"I have a daughter" does mean you have only one, though it's correct to ask "do you have a daughter" if you're not sure if the person has one, none, or multiple daughters. The correct answer is "yes, I have two daughters."
In common usage, the question "do you have a daughter" usually carries with it an implied elaboration in the response, since "a" does NOT literally mean "one" in this context.
If you had one daughter, a typical response might be "yeah, a 9 year old girl" or "I do, she's in college", or simply "yes, I do".
If you had two or more, you might say "I have two of them, a 9 year old girl and another in college" or just "two of them".
If I had to put a rule to how it's commonly used (in my experience), I'd say:
for 0 daughters, say that you do not
for 1 daughter, say that you do, and a small piece of information as well, such as her age or any basic descriptor
for 2 or more daughters, it's acceptable to just say how many you have, with any extra information being completely optional to include
On its own, "I have a daughter" does mean "I have one daughter". (An exception might be if you've just now got/learned of the newest daughter, by birth or prenatal testing results or adoption or a transgender announcement.) In response to the question "Do you have a daughter?", "no" alone means "I have zero daughters."
Other than that, the answer will depend on the reason for the question. As it happens I do have two daughters, but won't always say that if the person is clearly only asking about one of them, or if one is enough.
"I saw a teenager who looks just like you. Do you have a daughter?" "yes" "I'm seeking the opinions of mothers of girls for a study. Do you have a daughter?" "yes"
If the person is asking in a conversational way, an answer of just "yes" would be almost as weird as an answer of "no". It would be appropriate to say something about my daughters and ask about theirs.
"Do you have a daughter?" "Yes, two in fact, they're 16 and 19."
I skimmed other answers and didn't find any mention of articles, so I'll just add some information about grammar:
The word a in English is an indefinite article. It is used in the following situations:
before phrases of time and measurements (per week/weekly)
I go to English class 4 times a week
- you can also use per week here
before phrases of jobs
I am a doctor
with a noun complement
Do you have a daughter? Yes, I have a daughter
- This is your case
- Note that if you have more than one daughter, you would start numbering how many: I actually have three daughters!
before phrases of nationality (very rarely)
He is an American
- This is not used often, only when the nationality is being used as a noun phrase (as used above). Some more examples/exceptions:
- She is a native French speaker (the noun phrase is in bold).
- She is a French
- This is incorrect because French is being used as an adjective to describe the woman; it is not a noun phrase
half/quite with a noun phrase
He is quite a handsome man
The recipe requires half a cup of sugar
To expand on the answer mentioning indefinite articles...
The words "a" and "an" are indefinite articles. By definition, this means that they do not refer to a specific quantity - "a" and "an" mean "at least one". The word "the" is called a definite article, and refers to a single entity.
A native English speaker will never, in seriousness, ask that question on its own with the intention of asking if you have exactly one daughter.
Yes this does mean you have ONE daughter. If you were asking how many children someone had you would say "how many children do you have". This could mean single or multiple children!
As an algorithm:
Do you have a daughter?
---If (number of daughters) > 0 ---------YES ---Else ---------NO
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