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Solfe
2012-Apr-07, 03:44 PM
I have 3 questions question which I had a hard time answering. I am not looking for answer to the question, but more of advice on reading problems (I think!).

Q1:
"Find the midpoint of the line segment with the given end points
(8,4) and (2,10)
The midpoint of the segment is {Place for answer}"

Now, I know I am looking to do this

(xm,ym)=((x1+x2)/2,(y1+y2)/2)
The result should look like (a,b).
So, I think the answer is ((8+2)/2,(4+10)/2) = (5,7).

On this question, the website accepts the answer.

The very next question is in the exact same format and text with different numbers. Ok. I cannot get the right answer in three tries and the website shows the correct answer.

It appear that what is different is the presented numbers are not coordinates, but (x1,x2) and (y1,y2).

The third questions text and number different:
"Find the midpoint of the line segment with the following end points
(4,4) and (2,2)
The midpoint of the segment is {Place for answer}"

When I did this question, I assumed that the numbers presented were in the form (x1,x2) and (y1,y2) since the last question used that form. They weren't, so I assumed that they were (x1,y1) and (x2,y2) and that was the answer.

Sorry to be overly complicated and long, but is there anything in the English of those 3 problems that would indicate what each number represents?

profloater
2012-Apr-07, 03:51 PM
just a guess, but I think the second question had the typo you spotted since (x1,x2) is completely non standard format for this kind of question. So it was either just wrong or designed to frustrate you.

Solfe
2012-Apr-07, 06:00 PM
Pft. This website needs some serious quality assurance. It isn't ready to be called vaporware.

On the same website, I was asked how much a kilogram of material weights at various temperatures. The problem with that was the answer was in units of volume. Obviously, they wanted the volume of a kilogram of material at various temperatures but didn't ask that question.

Please by all means, ask students the wrong questions. If it wasn't twenty percent of each class grade, I would ignore the homework all together.

(Edit - I was really hoping that someone here would say "No, you read that wrong dummy." I could take that better than something that is actually wrong.)

HenrikOlsen
2012-Apr-08, 12:13 AM
On the same website, I was asked how much a kilogram of material weights at various temperatures. The problem with that was the answer was in units of volume. Obviously, they wanted the volume of a kilogram of material at various temperatures but didn't ask that question.
If they had specified a medium it just might have made sense, since a kilogram is the mass of the object not its weight and Archimedes law would apply as both the volume of the object and the density of the medium and thus the displacement changes with temperature, so the weight (not mass) will actually change minutely.

That they want the answer in volume units is what makes the question wrong.

grapes
2012-Apr-08, 01:01 AM
Give us the numbers, and the answer, for the second problem. Actually, why not the second problem verbatim?

orionjim
2012-Apr-08, 01:56 AM
...


(xm,ym)=((x1+x2)/2,(y1+y2)/2)
The result should look like (a,b).
So, I think the answer is ((8+2)/2,(4+10)/2) = (5,7).

...

AS SEANF POINTS OUT BELOW --- THIS IS WRONG------
With this you are calculating the midpoint of the line without regard to its location. The first example happens to work out fine. But the second example doesn’t.
All you need to do is an offset from the first point, something like this:
(xm,ym)=(x1-(x1-x2)/2,y1-(y1-y2)/2)

Or (8-(8-2)/2,(4-(4-10)/2) = (5,7)

the 2nd is:
(4-(4-2)/2,(4-(4-2)/2) = (3,3)

Jim

Solfe
2012-Apr-08, 02:54 AM
Give us the numbers, and the answer, for the second problem. Actually, why not the second problem verbatim?

Once I close the window, the question is marked as right or wrong. I can revisit the page, but it generates a new question where the text and format is identical, but the numbers change. This regeneration deletes my old answer and I have to answer it again to get any credit.

I will go back tomorrow and generate a few questions in a row to see what happens. I need the practice for a test on Wednesday. I just don't have any sanity left tonight.

SeanF
2012-Apr-08, 03:03 AM
...

(xm,ym)=((x1+x2)/2,(y1+y2)/2)
The result should look like (a,b).
So, I think the answer is ((8+2)/2,(4+10)/2) = (5,7).

...With this you are calculating the midpoint of the line without regard to its location. The first example happens to work out fine. But the second example doesn’t.
All you need to do is an offset from the first point, something like this:
(xm,ym)=(x1-(x1-x2)/2,y1-(y1-y2)/2)

Or (8-(8-2)/2,(4-(4-10)/2) = (5,7)

the 2nd is:
(4-(4-2)/2,(4-(4-2)/2) = (3,3)

Jim
I believe your equations and Solfe's equations are the same. (x1+x2)/2 and x1-(x1-x2)/2 will always give the same answer.

orionjim
2012-Apr-08, 04:53 AM
I believe your equations and Solfe's equations are the same. (x1+x2)/2 and x1-(x1-x2)/2 will always give the same answer.

Oooops, You are right!

DoggerDan
2012-Apr-08, 01:53 PM
It looks like a broken question to me. X-Y coordinates have always been presented in (x,y) format. Never (x,x).

grapes
2012-Apr-08, 02:01 PM
Without having the second question verbatim, the best two explanations, in order of probability, are 1) there was a mistake in the answer key, and 2) you made a mistake, and are mis-remembering the problem.

To find a midpoint (using euclidean coordinates), just take the average of each coordinate, no matter how many coordinates there are.

Solfe
2012-May-31, 03:44 AM
Well, I survived this class with a C. Sorry I never followed up.

There was an amusing/evil ending to this story. In the last week of class, the teacher "unlocked" all of the tests and homework so that we could take them as many times as we wanted for credit. There were a couple of downsides to this:

1) Only the last test counted, not the highest grade.
1a.) If you had a 96% on a test, it was a gamble to go back and retake it for the one question you missed. A typo or two and you are worse off.
2) Each test was 25 questions long, but each time you took it the order of the questions changed.
3) The values in each question changed, but for the most part the format of each question was the same.
4) Sometimes the requested answer was slightly different. One test may ask you to solve for X and the next time it ask you to solve for Y.
5) Homework was much easier, all correct answers stayed leaving only incorrect problems to be reworked.

I got the impression that the teacher is completely revamping how he does things next semester. He must have a new book and software.

grapes
2012-May-31, 10:59 AM
My daughter is taking a test today, and she's been using study books. Egregious errors: one question had identical answers for the A and B choices, one was right according to the key; another question explained why B was the correct choice--by explaining that the answer was the one listed under C; another explanation had nothing to do with the problem at all.

Nothing like preparing for the real world, eh?

swampyankee
2012-May-31, 12:16 PM
My daughter is taking a test today, and she's been using study books. Egregious errors: one question had identical answers for the A and B choices, one was right according to the key; another question explained why B was the correct choice--by explaining that the answer was the one listed under C; another explanation had nothing to do with the problem at all.

Nothing like preparing for the real world, eh?

Not uncommon -- I have study guide for a Praxis II (teacher certification test) which has one question where none of the choices are correct. Personally, I hate giving multiple choice tests. They're easy to grade (right vs wrong is binary) but they're also easy to game1, and it's quite difficult to write one.


--------------------------

1: One interesting factoid is that, historically, on the verbal SAT (one of the de facto college admissions tests in the US) the longest answer is right 40% of the time. Chance would be 25%.

HenrikOlsen
2012-May-31, 12:33 PM
They're really easy to game, I remember we had one in uni in statistics where the teacher designed the answers such that if people used one of the two common calculators of the time, they would have rounding errors which gave one of the two incorrect answers, while a correct analytical reduction of the question before using the calculator would give a third answer which was the correct one

Of really nasty questions, I liked this one when I saw it:

If you answer this test randomly, what is the chance of getting it correct?
A: 25%
B: 33%
C: 25%
D: 50%

DonM435
2012-May-31, 12:48 PM
In grad school (Educational Research) I took several courses in test construction, and we had huge files of bad test questions, so believe me, I knew these. With enough practice in testmanmship alone, you can do well on a badly-written multiple-choice test knowing practically nothing about the subject matter.

While unemployed in South Carolina in the 1970s (Jimmy Carter years), I took several dozen of "merit tests" to qualify for state jobs. Most were for personnel-type gigs, but there were some technical openings. There was a process for pointing out unfair test items, and I wrote these up regularly, making solid recommendations for improvement.

I took one test for something like "Research Analyst III," and in the mail received a response that the scoring of this exam would be delayed for some weeks due to recalibration. After the recalibration, my score was something like 99.82 out of 100. Now: (1) Whom do you think prompted the recalibration? and (b) Did these people offer him or her a job at once? Answers: (1) I have no idea; and (2) No.

This was just one qualifier, and of course there were other factors for hiring people. All of my 95+% scores got me into the top ten for interviews, but no job offers.

I had to pull some strings to get one outside the system. The good old American Way.

SeanF
2012-May-31, 02:02 PM
Of really nasty questions, I liked this one when I saw it:
If you answer this test randomly, what is the chance of getting it correct?
A: 25%
B: 33%
C: 25%
D: 50%
The answer is 0%, it's just not one of the offered choices. Change B to 0%, and then there's actually no answer. :)

Moose
2012-Jun-01, 10:56 AM
If you answer this test randomly, what is the chance of getting it correct?
A: 25%
B: 33%
C: 25%
D: 50%

The answer is 25%. If you are answering randomly, then the substance of each choice has no bearing on your answer, and so each choice remains equally guessable. If the fact that there are two unique answers with identical meanings in any way influences your answer, it isn't a random choice anymore.

Ironically, if you are permitted to discriminate against the 25% answers so long as the rest of the guess remains random, then the correct answer is D: 50%.

ShinAce
2012-Jun-01, 01:03 PM
Assuming all questions are ABCD, it would be 25%, but they listed two of the answers as 25%.

I've had multiple choice exams where multiple answers were allowed. Didn't bother me at all, but many students were not happy. I imagine they like to guess.

SeanF
2012-Jun-01, 02:08 PM
The answer is 25%. If you are answering randomly, then the substance of each choice has no bearing on your answer, and so each choice remains equally guessable. If the fact that there are two unique answers with identical meanings in any way influences your answer, it isn't a random choice anymore.

Ironically, if you are permitted to discriminate against the 25% answers so long as the rest of the guess remains random, then the correct answer is D: 50%.
The answer must be x% such that you have an x% chance of randomly choosing x%.

If you randomly choose an answer from the four given, the odds are 50% that you'll randomly choose 25%. So, 25% can't be the answer.

And if you're permitted to discriminate against the 25% answers, the odds are 33% that you'll randomly choose 50%. So, 50% can't be the answer in this case, either.

BioSci
2012-Jun-01, 03:53 PM
The answer must be x% such that you have an x% chance of randomly choosing x%.If you randomly choose an answer from the four given, the odds are 50% that you'll randomly choose 25%. So, 25% can't be the answer.

And if you're permitted to discriminate against the 25% answers, the odds are 33% that you'll randomly choose 50%. So, 50% can't be the answer in this case, either.

But: it actually depends on how the concept of "correct" is to be used for the test:
a) was there additional test instructions regarding how to select answers (only one, best answer, best answers, no answer, etc?) - known examples of a "meta-test" of one's ability to follow instructions...
b) the "correct" answer is the one specified in the answer key (even if "wrong") - we have all been there!
c) make up your own likely assumptions ...
d) the instructor is messing with student's logical abilities

if a) then one might be able to select an answer if further instructions could provide a logical result...
if b) then the chance of randomly selecting the "correct" answer is 25% but there is no logical reason to expect that any particular answer (A,B,C, or D) is the"correct" answer as found in the key.
if c) good luck!
if d) bingo!

grapes
2012-Jun-01, 04:28 PM
It's a joke/paradox/puzzle.

It's easy to build self-referential inconsistencies into questions. Like "If the red apple is green, what color is it?" Others are more subtle, like if you allow the definition of omnipotence to include both "can 'do something'" and "can 'not do something'". Can an omnipotent being create a rock so big it cannot lift it?

In this question, the assumption of randomness means that the probability of choosing any of ABC or D is 25%, no matter what. The contents of the answers have been adjusted so that there is no right answer. A less subtle version of the puzzle would have all the answers be "37%"--still no right answer.

I'm not sure what you mean, SeanF, about being able to discriminate against the two "25%" answers. But if you mean, change the probability that they be chosen, then one possibility is that you can avoid them entirely (this is a new and different problem), which means there are only two possibilities and the probability of picking either of the other answers is 50% and there is a right answer.

SeanF
2012-Jun-01, 04:34 PM
In this question, the assumption of randomness means that the probability of choosing any of ABC or D is 25%, no matter what. The contents of the answers have been adjusted so that there is no right answer. A less subtle version of the puzzle would have all the answers be "37%"--still no right answer.
I disagree slightly with this. The contents of the answers have been adjusted so that the right answer is not one of the listed choices, but there still is a right answer. In both the original case and your 37% variation, the right answer is 0%. If the puzzle is modified as I said so that 0% is one of the listed choices, then there is no right answer.


I'm not sure what you mean, SeanF, about being able to discriminate against the two "25%" answers. If you mean, change the probability that they be chosen, then one possibility is that you can avoid them entirely (this is a new and different problem), which means there are only two possibilities and the probability of picking either of the other answers is 50% and there is a right answer.
That was originally Moose's choice of words, so you'll have to ask him what it means. I took it to mean that the user could treat the two identical choices as a single choice, thus reducing the options to three with a 33% probability of each.

If you can "change the probability" that any particular options are chosen, then anything could be the "right" answer, couldn't it?

Jim
2012-Jun-01, 04:53 PM
I've been taking Computer Based Training (CBT) for work. After each "course," they give you a test. The test questions are randomly selected by the computer from a pool of questions. I'm thinking the answers are randomly listed as well.

Case in point, one question had four answers. You could only select one.

a) wrong answer
b) wrong answer
c) none of the above
d) right answer

You can ony select one.

ShinAce
2012-Jun-01, 04:57 PM
Seems like an exercise in Bayesian logic. First, we notice that the question has 4 options and we are to choose a single option. Assuming only one answer is the correct answer, there's a 25% chance of randomly choosing it.

Now we look at the answers. Two of them say 25%, which we know is the correct answer. "Knowing" the answer is what allows us to modify the odds. Since 1/2 of the choices are the correct answer, there's a 50% chance that we would randomly select A or C. To this specific question, the answer is 50%. It's a lot like the Month Hall problem. Getting additional information changes the odds. More formally known as Bayesian probability.

You could modify the question by just changing the answers:
A) 100%
B) 33%
D) 50%
D) 0%

or even:
A) 25%
B) 25%
C) 25%
D) 75%

In all cases, I choose D.

BioSci
2012-Jun-01, 05:16 PM
Now we look at the answers. Two of them say 25%, which we know is the correct answer. "Knowing" the answer is what allows us to modify the odds. Since 1/2 of the choices are the correct answer, there's a 50% chance that we would randomly select A or C. To this specific question, the answer is 50%.

But the answer of 50% is an answer to a different question (one that was not asked) - as you indicated the correct answer to the question that was asked is 25% - and that is based on the assumption that there is a single "correct" answer.

Perhaps the best answer is: E) 20%

BioSci
2012-Jun-01, 05:30 PM
Then one has an additional problem:

If you answer this test randomly, what is the chance of getting it correct?


The question specifies "test" and therefore the correct answer would be (1/4)^n where n is the number of questions...

ShinAce
2012-Jun-01, 05:32 PM
But the answer of 50% is an answer to a different question (one that was not asked)

Perhaps the best answer is: E) 20%

1) I'm assuming the question says "If you answer this question randomly, what is the chance of getting it correct?". You're being asked this question, not another one. You have to work with this one. We assumed that we can only choose one answer and that the correct answer would not be repeated. We can still only choose 1, but we see that the correct answer is repeated. You must now change your answer.

2) Same as 1). E is not an option and is not part of the question.

I had a good one on a stats exam. It basically went as:
"Three airports(A, B, and C) have odds of detecting weapons of (0.4 , 0.6, 0.9) respectively. A person was caught with a knife at one of the three airports. What are the odds that they were caught at airport B?".

A person was caught is a big red flag that this is a Bayesian probability question. We have to adjust for the odds that the person had a knife and was not caught.

Another example was the OJ Simpson trial. It was known that OJ had been charged with domestic violence. The defense argued that less than 1% of women that are domestically abused were killed by their spouse. The problem is that Nicole had already been murdered. The odds of a domestically abused woman found dead to have been killed by their spouse is 90%.

It's a really cool concept that applies to things like medical test accuracy, actuarial science, and so forth. This is going beyond the intended scope of the thread though, so I'll leave it alone for others to explore themselves.

I'd suggest starting with the Monty Hall problem. It's classic!

SeanF
2012-Jun-01, 06:29 PM
...Two of them say 25%, which we know is the correct answer...
...To this specific question, the answer is 50%...
There's only one question, and the correct answer cannot be both 25% and 50%.


It's a lot like the Month Hall problem. Getting additional information changes the odds.
But the question asks what the odds are. If you change the odds, you change the answer to the question.


You could modify the question by just changing the answers:
A) 100%
B) 33%
D) 50%
D) 0%

or even:
A) 25%
B) 25%
C) 25%
D) 75%

In all cases, I choose D.
The question can be reworded as:

"On this question, you have an x% chance of randomly choosing an answer which says 'x%'. What is x?"

Option D does not work in either case.

grapes
2012-Jun-01, 09:40 PM
I disagree slightly with this. The contents of the answers have been adjusted so that the right answer is not one of the listed choices, but there still is a right answer. In both the original case and your 37% variation, the right answer is 0%. If the puzzle is modified as I said so that 0% is one of the listed choices, then there is no right answer.
Yahbut, I interpret it slightly differently. :)


That was originally Moose's choice of words, so you'll have to ask him what it means. I took it to mean that the user could treat the two identical choices as a single choice, thus reducing the options to three with a 33% probability of each.

If you can "change the probability" that any particular options are chosen, then anything could be the "right" answer, couldn't it?Pretty much, that was the point that I was making.

The question can be reworded as:

"On this question, you have an x% chance of randomly choosing an answer which says 'x%'. What is x?"
There, that's where I would differ. Instead of "What is x?" shouldn't it be "What is the letter of the answer that says "x"?

After all, the answer to the question is A, B, C or D, not x. :)

SeanF
2012-Jun-01, 09:53 PM
There, that's where I would differ. Instead of "What is x?" shouldn't it be "What is the letter of the answer that says "x"?

After all, the answer to the question is A, B, C or D, not x. :)
The original question, as Henrik posted it, asked "What is the chance...?" B is a letter, not a chance, so it can't be the answer to the question.

There are four answers offered to choose from, and the letters A-D are nothing more than labels. :)

EDIT: I'm not sure it matter, though. If you're going to do it that way, then you'd also change my rewording of the question to say "There is an x% chance that you would randomly choose the letter of the answer that says 'x%'". With Henrik's original possible answers, as well as with your 37% option, the only value of x that works is 0, and there's no letter to go with it.

With my choices (25%, 0%, 25%, 50%) or Shinace's first option (100%, 33%, 50%, 0%), there is no value of x that works at all.

grapes
2012-Jun-01, 10:38 PM
There are four answers offered to choose from, and the letters A-D are nothing more than labels. :)
Sure, true. And I meant it that way, of course--answering the question randomly, you choose between the four possible answers, that's why the probability of any particular answer is 25%. Even though two answers have they same x, they are different answers. The A,B,C,D labels are what make them different.


EDIT: I'm not sure it matter, though. If you're going to do it that way, then you'd also change my rewording of the question to say "There is an x% chance that you would randomly choose the letter of the answer that says 'x%'". With Henrik's original possible answers, as well as with your 37% option, the only value of x that works is 0, and there's no letter to go with it.
And that's why I said there was no answer, whereas you said there was an answer. Isn't that the particular angel we're trying to stuff onto this pin? :)

Moose
2012-Jun-01, 11:47 PM
That was originally Moose's choice of words, so you'll have to ask him what it means. I took it to mean that the user could treat the two identical choices as a single choice, thus reducing the options to three with a 33% probability of each.

I intended it to mean that one would reject both 25% answers because of the paradox it creates, leaving only two answers, were someone to allow only a partially random pick.

SeanF
2012-Jun-02, 04:05 AM
And that's why I said there was no answer, whereas you said there was an answer. Isn't that the particular angel we're trying to stuff onto this pin? :)
Could be. :)


What is 2+2?

A. 1
B. 3
C. 5
D. 6

To me, the answer to the question is 4. To you, there's no answer?

SeanF
2012-Jun-02, 04:07 AM
I intended it to mean that one would reject both 25% answers because of the paradox it creates, leaving only two answers, were someone to allow only a partially random pick.
I see.

I'm not sure that the two 25% answers create a paradox all by themselves, but only in conjunction with the other choices, so I'm not sure there's a reason to eliminate them, but I'll have to think about it some more.

If the offered choices were 25%, 33 1/3%, 25%, and 50%, would you eliminate both 25% and make 50% the correct answer, or just eliminate one and make 33 1/3% the correct answer?

Moose
2012-Jun-02, 09:15 AM
If the offered choices were 25%, 33 1/3%, 25%, and 50%, would you eliminate both 25% and make 50% the correct answer, or just eliminate one and make 33 1/3% the correct answer?

Remember, the A choice is "A: 25%." This is distinct from "C: 25%". The meaning of each choice is the same, but the choices are distinct. If 25% is the correct answer, there's no way to determine which of A and C will be chosen by an auto-grader, thus (as Vizzini would likely say) he can clearly not drink either wine in front of you. Thus, 50%.

The paradox is that A and C can only be considered identical answers if 25% is the correct answer. Otherwise, they're both wrong and don't really affect the probability at all. But if 25% is the correct answer, and you're merging their probabilities, then the correct answer can no longer be 25%. So neither A nor C can be correct, and neither can be incorrect. Paradox.

The implications of that go much further ("I'm just getting started!"), but I won't get into it 'cause, you know, the iocaine powder.

Tobin Dax
2012-Jun-02, 10:17 AM
Truly, you have a dizzying intellect.

grapes
2012-Jun-02, 12:08 PM
What is 2+2?

A. 1
B. 3
C. 5
D. 6

To me, the answer to the question is 4. To you, there's no answer?Right!

We're using two different meanings of the word "answer".

I'm using the problem specific meaning of answer--what is the probability of choosing the right answer? If that probability is assumed to be 25% for each choice, we must be considering four answers. But, we know that 4 is a fifth answer. Are there four answers, or five answers? Actually, if 4 is also an answer, we'd also have to include all numbers as answers.

You might say, there is only one answer. That's a third, and different, use of the word. (ETA: in summary, we have answer(ABCD, all possible responses to the test), answer(all possible numbers, in other words, all possible responses outside of the test), answer(the correct solution) )

I'm not saying your use of the word "answer" is wrong, it is just different than mine.

Moose
2012-Jun-02, 01:19 PM
Truly, you have a dizzying intellect.

NEVER go against an Acadian when MATH is on the line!

ShinAce
2012-Jun-02, 01:58 PM
NEVER go against an Acadian when MATH is on the line!

Or a drinking game...

DoggerDan
2012-Jun-04, 09:06 AM
This thread reminds me of "How many elephants would it take to get from New York to San Diego in less time than Aunt Dolores likes the Beatles?"

HenrikOlsen
2012-Jun-04, 09:49 AM
My take on it is to separate the labels (ABCD) from the values (25%,33%,50%) and go:

If choosing A is correct, then so is choosing C, because they have the same value. If choosing A or C is correct, the chance of picking a correct answer is 50%. Since this is not the value of A and C, they can't be correct.
If choosing B or D is correct, the chance of picking the correct answer is 25% and since neither has that as the value, neither can be correct.
Which means there are no correct choices.

Jeff Root
2012-Jun-04, 12:14 PM
Henrik,

How much time and effort did you expend to get that
explanation? I'm wondering if it came to you easily
and quickly or if you had to work at it and refine it
bit-by-bit. It seems very good, very concise.

-- Jeff, in Minneapolis

HenrikOlsen
2012-Jun-04, 02:01 PM
I posted the explanation the place I saw that test too, and there it took about half a minute to get the complete solution and about 10 minutes to write the explanation with lots of rewrites (something I do with most posts anyway).
This time it was easy and quick to write because it was already condensed to understanding a while ago.

The main rewrite here was to distinguish "choosing" and "picking randomly" explicitly.

DonM435
2012-Jun-05, 01:35 PM
I've been taking Computer Based Training (CBT) for work. After each "course," they give you a test. The test questions are randomly selected by the computer from a pool of questions. I'm thinking the answers are randomly listed as well.

Case in point, one question had four answers. You could only select one.

a) wrong answer
b) wrong answer
c) none of the above
d) right answer

You can ony select one.

We were taught to (if indeed you use this type of construction) to place "All of the above" in the penultimate slot and "None of the above" in the final one. Otherwise, the "All" would seem to include the "None" so that the earlier options are both supported and negated at once.