You will be given a trivia clue, and the category it belongs to. You should answer with the best answer that belongs in the category and is described by the clue. For simplicity, answers should be in all lower cased letters.

Category: CARMEN 
Clue: It's the capital city where "Carmen" composer Georges Bizet was born in 1838
paris

Category: 20th CENTURY ART 
Clue: Russian-born artist whose work is seen here:
marc chagall

Category: OPERA TITLE CHARACTERS 
Clue: If this heroine had married Prince Yamadori, there might not be that nasty suicide in Act III

madame butterfly