2. Applied The hit new social media site FOL-owo Me involves users following users' posts. This social media site can be represented as the tuple (S,F) where S denotes the set

of all the users in the site and F denotes the set of ordered pairs for who follows who. Meaning we can think of S as a unary predicate and F as a binary predicate. For example, (Mac, Excellent Elf) = F means Mac follows Excellent Elf. In FOL-owo Me, the follow restriction holds: Vavy(Fry → (Sx ^ Sy)). Users can follow as many users (including themselves) as they wish. (a) Draw out a sample instance of FOL-owo Me with at least 4 users and at least 5 ordered pairs in F. Give the users family-friendly names. (b) Assume the worst-case scenario for the servers - Everyone is following everyone (including themselves!). Prove by mathematical induction on the amount of users S, that |F|≤|S|². Hint: Think of the smallest number of users in the system, and think of how many more follows are added when we add a new user following everyone.