Test the validity of the following syllogisms by the traditional method of rules and fallacies, after arranging them into standard form(wherever necessary):
1) No Doctors are extremists and some extremists are violent persons.It follows, some violent persons are not doctors.
2) All applicants are degree holders and Sam is an applicant,hence Sam is degree holder.
3) Since all dictators are ruthless and no ruthless is lover of art,so no dictator is lover of art.
4) Some games are played for entertainment and some games are played for making profit,which implies some entertainment acts are for making profit.
5) No Indian is Greek but some Indians are Aryans,therefore some Greeks are not Aryans.