English, 12.03.2020 20:55 joshvslogic341

You are a lonely logician in desperate need of a friend. However, knowing that it would be impossible to make one, you decide to focus your time on something much more achievable: creating a general AI (artificial intelligence) who will then be your friend! Amazingly, you succeed! You make yourself a friend whom you name Alan. Now all you need to do is teach Alan what "friendship" is. You decide to model "friendship" as a relation on a set of people. Rather than explicitly define the relation, you decide to explain some rules that any relation modelling friendship must follow. These are your three laws of robotic friendships:

1. "Not everyone is friends with everyone" (as you harshly know from your lack of human friends).
2. "The enemy of my enemy is my friend" (this is a good saying you've heard before! For simplicity, you tell Alan "enemy" just means "not friend").
3. "The enemy of my friend is my enemy."

Does Alan think "friendship" is an equivalence relation? Explain why or why not. If it is, how many equivalence classes does it define on a set of 100 people? Explain in English how you arrived at your answer.

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You are a lonely logician in desperate need of a friend. However, knowing that it would be impossibl...