13) Five people do not agree on the date.

- Carlo says that today is Monday, August 16
- Franco says that today is Tuesday, August 16
- Marco says that today is Tuesday, September 17
- Roberto says that today is Monday, August 17
- Tullio says that today is Monday, September 17.

One is right, but no one is "completely" wrong, in the sense that each one correctly states at least one thing (either the day of the week, or the day of the month, or the month). Who is right?
(A) Carlo
(B) Franco
(C) Marco
(D) Roberto
(E) Tullio.
13) The answer is $\mathbf{( D )}$.

The statements of Carlo and Marco have no element in common, so if one of them were right, the other would be "completely" wrong. The same applies to the statements of Franco and Tullio. Therefore, Roberto is right, whose statements have at least one element in common with those of his friends.

On the other hand, assuming Roberto's statement is true, it is easily verified that each of the others has said something true.