Since I'm travelling and I'll be away from a computer until after the deadline, I'll just copy/paste my answer below to ensure you can access it, Fish. Sorry for the length.
What is the most correct way to respond to a multiple choice question that provides no correct answer?
A: Choose the next best thing.
B: Refuse to answer.
C: Guess
D: Ask for help
While I hope that my students would choose D, that would be a self-defeating answer in this particular case. I'm forced, then, to choose A.
The most correct response is: A
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What statement must logically be correct?
A: Answer C is true.
B: Whatever remains, if anything.
C: Answer A is true if answer E is not true.
D: Logic does not apply here.
E: None of the answers given are correct.
Let's start with D, because it's deceptively tricky. It involves what's called an indexical ('here') that is ambiguous. It could mean (1) here, as in that particular statement or (2) here as in the entire question. Since (2) is patently false (C can be captured in a formal logic system) we can safely conclusion that D is not logically correct on this reading. As for (1), the statement becomes self-defeating and thus cannot be correct. So 2 need not be logically correct.
We can easily ignore B as there's no clear way to capture this logically. Putting this as a clear conditional, we get: 'If anything, whatever remains.' This fails to carry any semantic value. The key question is whether the statement *must* be logically correct. There are domains of interpretation under which this statement *could* be correct. But it certainly doesn't follow that such statements *must* be correct.
Let's now turn to the relationship between A, C and E. We'll start by making the assumption that E is correct--i.e. that A-D are all incorrect (we'll also give a charitable reading here that E is not self-referring and thus self-defeating. As we'll see, this assumption ultimately won't matter).
With that assumption in place, we have E as a true statement. Looking at C, we can reformulate this as: If E is not true, then A is true. The problem now is that the conditional that is C is going to be necessarily true; any conditional with a false antecendent will be true. It doesn't even matter whether A is true or false. Since C is now necessarily true, we have a contradiction with E, which says that none of the statement are true. This tells us that our assumption that E is correct is false!
With E being false, that means at least 1 statement must be true/logically correct. Looking back at C, the antecedent is now true. Just a reminder, C says that 'If E is not true, then A is true.' For this statement to be true, then, A must be true.
Of course, this statement could be a false one, which would be that A is false. A says that C is true but, as we've seen, having all false statements would result in a contradiction, since this would end up making E true (and we've already seen that the state of affairs there results in a contradiction). The only logical possibility is to make C true, which would imply that A is true.
Thus, the 2 statements that *must* be logically correct are: A and C.
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Which direction is left?
A: Perpendicular to the z-axis.
B: Three rights
C: Away from the centre of mass.
D: Tangential to the surface represented by the equation 1=x^2 + y^2 + z^2
E: Other, please specify
The answer here is E: Other, please specify.
Since 'left' requires a preferred reference frame (which is disallowed on the Standard Model), the question must mean left as in 'remaining' or 'left over'. In this case, there are an infinite number of directions remaining--in particular, extra-dimensional directions. For ease, I'll just stick with an n-1 dimensional line that would be tangential to an n-dimensional sphere, where n > 3.
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Which statements below are not true?
A: Answers A and B are false.
B: Answer A is true.
C: All answers except D.
D: All of the above are true.
E: None of the above are true.
Statement A must be false, since paradoxes would ensue. This also implies that B is false as well. Answer C (on a charitable reading) says that D is true, which would contradict C. So C and D are both false. E, however, is a true statement--A-D all fail to be true.
The statements that are not true are: A, B, C and D.
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If an instruction or command appears to be posing as a question, choose the correct response.
A: Treat it like a question.
B: Refuse to answer.
c: Is this a trick question?
D: LOL u nOOb
E: Ignore this last option. It does nothing.
This item itself is an instruction that appears to be posing as a question. The key phrases here are 'appears' and 'posing'. In other words, it appears to you as if the statement is pretending to be a question, but isn't. A more ordinary example of this kind of statement would be, "Could you shut the door?" or "Can up pick up some milk on the way home?" These are commands (really, requests) that appear to be posing as questions, but they're not actually questions.
Of course, one could be wrong in this assessment. But in order to remain consistent with one's beliefs, we should exclude A. Treating it like a question would be a ****** move and would be inconsistent with what you believe. This fails on the criteria of moral and epistemic correctness.
It turns out, though, that on any reading of the question, the correct answer is C. This could be a meta-level question (one which refers to itself) which would mean it's a trick question, since it's formed as a trivially true conditional. But if there is genuine confusion about the status of a question, then C would still fit with one's beliefs and moral duties when asked to do something.
So the correct response is: C
