sentence1: I see the rather boring point about using alumni to cover both men and women, and I quite agree that the use of relatively newer and less widely used terms like authoress, aviatrix , and poetess seems to be a deliberate, unwarranted attempt to identify someone as a female; but a graduate of the feminine gender is a `woman graduate' = alumna , the `first woman dancer in a ballet company' is a prima ballerina (I've never heard of a  prime ballerino ), and a `woman opera star' is a diva or prima donna .  I hesitate to point out that we use prima donna of men, too, because my critics will say that they disapprove of the term's second life as designating a  temperamental person of either sex.
sentence2: A prime ballerino is the 'first male dancer in a ballet company' and false is not true .