People and Clubs: An Axiomatic System The town of Hilbert has an interesting club system. Each club is a list of townspeople and no two clubs have exactly the same membership list. Here are the important rules regarding the clubs that are followed by every person in town and every club: 1. Every two people have exactly one club that they both belong to; 2. Every club has at least two members; 3. No club contains all the townspeople; 4. If you choose a club and then choose a person who is not a member of that club, there is exactly one club that person belongs to that has no members in common with the club you chose. 1.6 Using inductive reasoning, form a conjecture for the number of clubs in a town of Hilbert with n people that you believe to be true. a. Demonstrate your inductive reasoning. b. Write your conjecture in the form of a conditional statement. C. Write the converse, inverse, contrapositive, and bi-directional forms of your statement, and explain whether or not you believe each of these forms to be true. People and Clubs: An Axiomatic System The town of Hilbert has an interesting club system. Each club is a list of townspeople and no two clubs have exactly the same membership list. Here are the important rules regarding the clubs that are followed by every person in town and every club: 1. Every two people have exactly one club that they both belong to; 2. Every club has at least two members; 3. No club contains all the townspeople; 4. If you choose a club and then choose a person who is not a member of that club, there is exactly one club that person belongs to that has no members in common with the club you chose. 1.6 Using inductive reasoning, form a conjecture for the number of clubs in a town of Hilbert with n people that you believe to be true. a. Demonstrate your inductive reasoning. b. Write your conjecture in the form of a conditional statement. C. Write the converse, inverse, contrapositive, and bi-directional forms of your statement, and explain whether or not you believe each of these forms to be true