5. You are at a party attended by n people (not including yourself), and you suspect that there might be a celebrity present. A celebrity is someone known by everyone, but does not know anyone except herself/himself. (Of course everyone knows herself/himself). Your task is to work out if there is a celebrity present, and if so, which of the n people present is a celebrity. To do so, you can ask a person X if they know another person Y (where you choose X and Y when asking the question). (a) [10 marks] Show that your task can always be accomplished by asking no more than 3n 3 such questions, even in the worst case. Hint: Assume you ask A if he knous B. If the answer is yes what can you conclude about A? If the answer is no uhat can you conclude about B? (b) [5 marks] Show that your task can always be accomplished by asking no more than 3n- log2 nJ-2 such questions, even in the worst case