Problem 4. (20 points) A guest at a party is a celebrity if this person is known by every other guest, but knows none of them. There is at most one celebrity at a party. Your task is to find the celebrity, if one exists, at a party by asking only one type of question: asking a guest whether they know a second guest. Everyone must answer your questions truthfully. That is, if Alice and Bob are two people at the party, you can ask Alice whether she knows Bob; she must answer correctly, Use mathematical induction to show that if there are n people at the party, then you can find the celebrity, if there is one, with 3(n-1) questions. Hint: First, ask a question to eliminate one person as a celebrity. Then use the inductive hypothesis to identify a potential celebrity. Finally, ask two more questions to determine uwhether that person is actually a celebrity