The following statements are either true or false:

*A. There are five lettered statements in this post.*

*B. This is not a statement.*

*C. Only two of these statements are false.*

*D. Only one of them is true.*

*E. The Holocaust never happened.*

Advertisements

This is adapted from the highly recommended book Superior Mathematical Puzzles. (http://books.google.com/books?id=YHksNY1SkWEC&pg=PA42#v=onepage&q&f=false)

yes..? I feel like C discredits B and D

But what if statement E were replaced with a contradiction, such as “Black is white”?

This is my third try at writing a reply haha. The previous two times I decided was a poor approach. However I always want to start with Statement C. It was kind of tricky, not having had any formal logic theory. I think I have a hard time from trying to figure out how to use C.

Condition for C implies C MAY BE true if 2 others are false. In fact it can be false, because the 2 others + C would mean 3 false. This also implies when C is false there cannot only be one other false and vice versa.

Our base case(?) is E is false, meaning at least one statement is false. That means if C is false there must be other incorrect statements. If C is true, there must be exactly one other false statement.

C and D cannot both be true, but can both be false. A and B are contradictions, one and only one must be true, I believe. If that’s the case, then There are automatically at least 3 falses (A/B, C/D, E), meaning C must be false. Now we have figured out 2 of the 5 statements to be false, and there must be one more (as noted previously and as C reminds us).

D says one statement is true. D can only be true is all else are false, because D points to itself. This is not true because A or B must be true. D is false, and thus CDE are currently false. But…one of A or B must be true…then D is true….contradiction..

Also, I just realized if B is not a statement, then it can’t state what it states, thus it is a statement. The statement is a pardox itself..isn’t it? I’m broken. xD

This post, in fact, purports to be a proof of statement E. If all five statements are logically valid, then they force E to be true. However, that’s the catch: this is why self-referential or circularly self-referential statements can’t be valid in axiomatic logic. It’s a more complex version of the Liar Paradox – basically saying “Either this sentence is a lie, or E is true.”