I received this question from my mathematics professor as a leisure-time logic quiz, and although I thought I answered it right, he denied. Can someone explain the reasoning behind the correct solution? Which answer in this list is the correct answer ...Read more

I received this question from my mathematics professor as a leisure-time logic quiz, and although I thought I answered it right, he denied. Can someone explain the reasoning behind the correct solution?

Which answer in this list is the correct answer to

thisquestion?

- All of the below.
- None of the below.
- All of the above.
- One of the above.
- None of the above.
- None of the above.

I thought:

- 22 and 33 contradict so 11 cannot be true.
- 22 denies 33 but 33 affirms 2,2, so 33 cannot be true
- 22 denies 4,4, but as 11 and 33 are proven to be false, 44 cannot be true.
- 66 denies 55 but not vice versa, so 55 cannot be true.

at this point only 22 and 66 are left to be considered. I thought choosing 22 would not deny 11 (and it can’t be *all of the below* and *none of the below*) hence I thought the answer is 6.6.

I don’t know the correct answer to the question. Thanks!

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