It's always possible to answer a closed-ended question in the negative. An obvious example would be "are you the Queen of England?" You can answer it in the negative unless you, of course... you get the point.
But, more broadly, a few of my questions are getting dismissive comments and attitudes because it is presumed that I am attempting to ask open-ended questions which cannot be answered in the negative (because completely-open-ended questions indeed cannot be proved to have a negative answer).
But the more narrow the scope of a question is, the easier it is to answer it in the negative.
Here's a few examples of open-ended questions:
- were there any days on which the temperature in the US dropped below -100 degrees F
- are there voters who always vote for the Republicans even though they are left-handed lapsed Catholic transsexual lawyers?
Contrast them with these examples of closed-ended questions:
- were there any days on which the temperature in the US dropped below -100 degrees F in 1995
- are there voters who always vote for the Republicans even though they are left-handed lapsed Catholic transsexual lawyers licensed to practice in Rhode Island?
The last one is a bit tricky. It's actually a closed-ended question which may seem like an open-ended question at 1st sight. If there is a public registry of lawyers who can practice in Rhode Island (a very small state), then it would not be that hard to know if any of them meet all of the other criteria.
The fact is that there is a Galois connection between how many criteria a category must meet and how large that category happens to be. The more criteria must be met, the more restrictions it has. The more restrictions it has, the less members are in the category.
If the category is small enough, then it is not difficult to make statements of the kind "no member of this category meets condition X" because it's trivial to show that each single member of it does not meet that condition.
I've asked questions about highly-restricted categories trying to figure out if it is known whether certain political facts are true about their members. These can be easily answered in the negative if the answer is indeed a no. Each of these categories probably had less than 20 members. These were not open-ended questions. Please, stop treating them like they were.