Problem:
A sealed envelope contains a card with a single digit on it. Three of the following statements are true, and the other is false.
I. The digit is .
II. The digit is not .
III. The digit is .
IV. The digit is not .
Which one of the following must necessarily be correct?
Answer Choices:
A. I is true.
B. I is false.
C. II is true.
D. III is true.
E. IV is false.
Solution:
Since both I and III cannot be false, the digit must be or . So either I or III is the false statement. Thus II and IV must be true and is necessarily correct. For the same reason, must be incorrect. If the digit is and are incorrect, and if the digit is is incorrect.