Question

select the sentence that has correct pronoun usage. (points : 1) either your supervisor or the restaurant owner must give her permission for you to have new year s eve off. either your supervisor or the restaurant owner must give their permission for you to have new year s eve off.

Answer 1

The sentence that has correct pronoun usage is the second one - Either your supervisor or the restaurant owner must give their permission for you to have New Year's Eve off.
You must use their because you don't know whether they are male or female.