Problem: The following four statements, and only these, are found on a card:
On this card exactly one statement is false.
On this card exactly two statements are false.
On this card exactly three statements are false.
On this card exactly four statements are false.
(Assume each statement on the card is either true or false.) Among them the number of false statements is exactly
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since each pair of statements on the card is contradictory, at most one of them is true. The assumption that none of the statements is true implies the fourth statement is true. Hence, there must be exactly one true statement on the card. In fact, it is easy to verify that the third statement is true.