Disjunctive syllogism is a rule of logical inference says that if you have P v Q and ~P, you can conclude Q.
For example, suppose
“You are Donald Trump or you are watching this video.”
and
“You are not Donald Trump.”
are true. Then you can conclude that you are watching this video.
One important thing I do not discuss in the video is that if you have P v Q and ~Q, you can conclude P. Note that this trivially follows from the description above by using commutativity—i.e., you can commute P v Q into Q v P and apply the first example of disjunctive syllogism using ~Q to conclude P. Some professors may not recognize “P v Q and ~Q, therefore P” as legitimate and would instead require you to commute P v Q first. Check with the graders of your course for guidance.