Three chess players, Garry, Anatoly, and Vishy, competed for fun. Two of them won and one lost. Determine who won and lost by using the following clues.
Anatoly won his match if Gary lost his match.
If Gary won his match, then Vishy lost his match.
Anatoly lost his match if Vishy won his match.
Prove that the following statements are false:
1. The sum of two two-digit numbers is a three-digit number.