Which of the two following statements is True and which is False ?
The next statement is "False".
The previous statement is "True".
The first sentence is obviously false, since the second is not "False" but a rather longer one starting with "The previous statement...".
Similarly, the second sentence is also false, as the first one is not "True" but "The next statement...".
You should be careful with quotes!
PS. I was taught how (not) to use quotes this way: would you like reading in the paper that you were seen entering a "hotel" with your "wife", a "young", "healthy", "female"?