Final answer:
It is true that Antonio Vivaldi taught many illegitimate children of nobility, as he worked at the Ospedale della Pietà , where such young women were educated and trained in music.
Step-by-step explanation:
The statement that many of Vivaldi's students were illegitimate offspring of noblemen is considered true. Antonio Vivaldi was an Italian Baroque composer and violinist who worked for much of his career at the Ospedale della Pietà in Venice, an institution that cared for orphaned or illegitimate daughters of noblemen.
These young women received extensive musical training, and many of the musicians Vivaldi taught there were indeed considered illegitimate by the standards of the day.
In the context of the question, 'illegitimate' refers to children born outside of wedlock, which was a more stigmatized status at that time, as societal norms and laws (such as the Lex Julia from ancient Rome) harshly treated adultery and emphasized legitimate succession and family honor.