Formalize the following arguments and verify whether they are correct:

a) If Carlo won the competition, then either Mario came second or Sergio came third. Sergio didnt come third. Thus, if Mario didnt come second, then Carlo didnt win the competition.

b) If Carlo won the competition, then either Mario came second or Sergio came third. Mario didnt come second. Thus, if Carlo won the competition, then Sergio didnt come third.

c) If Carlo won the competition, then Mario came second and Sergio came third. Mario didnt come second. Thus Carlo didnt win the competition.