northern-lights

Can't edit. Explanation for 6 is incorrect as pointed above/below. Correct explanation is: Lets say 6 is True. This implies that 5 is False. If 5 is False, it means at least one of the above 5 - 1, 2, 3, 4 is True. But we've established above that all of them are False. So, 5 cannot be False. Hence, 6 cannot be True.

You're right, my bad. Negation of None of the Above is False is Some of the Above is True. I will modify my explanation.

I didn't see a logical explanation that explains why an option is correct or not, so here's one:

Q Which answer in this list is the correct answer to this question?

1. All of the below. 2. None of the below. 3. All of the above. 4. One of the above. 5. None of the above. 6. None of the above.

I'll assume "is the answer" to be "True" and "is not the answer" to be "False" in my explanations to make it more readable.

Lets say 1 is True. This implies - 2, 3, 4, 5, 6 are also True. Now, if 2 is True, then it means 3, 4, 5, 6 are False. This contradicts what 1 says. So, 1 cannot be True.

Lets say 2 is True. This implies - 3, 4, 5, 6 are False. If 3 is False, it means both 1 and 2 cannot be True. Since, we've assumed 2 to be True, 1 can indeed be False, so this is consistent. If 4 is False, then it means either less than one or more than one out of 1, 2, 3 are True. Zero out of 1, 2, 3 cannot be True since it contradicts our assumption of 2 being True. So either two or three out of 1, 2, 3 have to be True. Since, we've already established than 1 is False, that leaves 3 to be True along with our assumption of 2 being True. But 3 cannot be True since it contradicts 2. So 2 cannot be True.

Lets say 3 is True. This implies 1, 2 are True. We've already established that 1, 2 are False. Moreover, 2 being True will contradict 3 being True. So 3 cannot be True.

Lets say 4 is True. This implies that exactly one of 1, 2, 3 is True. We've already established that they are False. So 4 cannot be True.

Lets say 5 is True. We now know that 1, 2, 3, 4 are not True. So, this is consistent. We'll come back to this.

Lets say 6 is True. This implies that 5 is False. If 5 is False, it means all of the above 5 - 1, 2 , 3, 4 are True which we've found not to be True. So 6 cannot be True.

That leaves only 5 to be answer to the question.