# Axiomatic Systems Problem solving, touch question!! will give lifesaver review!

###### Question:

The town of Greendale has an interesting club system. Each club is just a list of townspeople and no two clubs have exactly the same membership list. Here are theimportant rules regarding the clubs that are followed by every person in town and every club: a) Every two people have a club that they both belong to, but it isunique, meaning that for each pair of people, there is only one such club. b)every club has at least two members. c)No club contains all the townspeople. d)If you namea club and then a person who is not a member of that club, there will be one and only one club that person belongs to that has no members in common with the firstclub.
Now, suppose that we have a valid club system in Greendale(where there are 4 or more people). Let X be a club with memebers {x1,...xn} and let Y1 be any other clubthat has x1 as a member. We know from Axiom (a) that none of x2,x3....,xn can be in Y1. So using axiom (d), we know that for each xi(i=2,....,n), there is a club Yisuch that xi is in Yi and Yi and Y1 have no members in common.
a)Draw a picture that depicts this situation.
b)Carefully prove that every person in Greendale belongs to exactly one of the clubs Y1, Y2,...,Yn.

#### Similar Solved Questions

##### During February, the old building was demolished at a cost of $240,000, and an additional$200,000...
During February, the old building was demolished at a cost of $240,000, and an additional$200,000 was paid to clear and grade the land. Construction of a new building began on March 1 and was completed on October 30. Construction expenditures were as follows:       &n...
Please Solve This Excel Worksheet and List your Formulas, and How you got your answers so that I can learn from what you did. Please take your time as I know this will take a while! K LM L B C D E F G H I J Use only a combination of text manipulation (i.e., MID, CONCATENATE, TRIM, etc.) and/or logic...
##### QUESTION 19 3 points S In the reaction Mg0(s) → Mg(s) + + 0.502(g) the enthalpy change AH*) is +6...
QUESTION 19 3 points S In the reaction Mg0(s) → Mg(s) + + 0.502(g) the enthalpy change AH*) is +602(AHP) kj mol. 1 and the entropy change (A5) is +109J k-1 mor1. Explain if the reaction is feasible at 1000K or 6000K? Berenrenh Arial QUESTION 19 3 points S In the reaction Mg0(s) → Mg(s) + ...
##### Gentle Ben's Bar and Restaurant uses 5,000 quart bottles of an imported wine each year. The...
Gentle Ben's Bar and Restaurant uses 5,000 quart bottles of an imported wine each year. The effervescent wine costs $3 per bottle and is served only in whole bottles because it loses its bubbles quickly. Ben figures that it costs$10 each time an order is placed, and holding costs are 20 percent...
##### The weighted mean of the numbers 204, 206, 207, and 208 is 207.2
The weighted mean of the numbers 204, 206, 207, and 208 is 207.2. How could I arrive at the weight (or possible weights) of the four numbers?...
##### QUESTION 5 a) Find and sketch the domain of the function f(x,y) = \n(x2 - y...
QUESTION 5 a) Find and sketch the domain of the function f(x,y) = \n(x2 - y +1) + VÝ +1. (5 marks) b) Evaluate eży sin(3x +2y) lim (x,y) (-2,3) 3x +2y (6 marks)...
##### The Lewis dot symbol for the bromide ion has ____ unpaired electrons.
The Lewis dot symbol for the bromide ion has ____ unpaired electrons....
##### 3.8 points An initial state before reaction of CH4 and Cl2 is shown in the figure....
3.8 points An initial state before reaction of CH4 and Cl2 is shown in the figure. Based on the balanced equation and the figure, what is the excess reactant? CH (8) + 4 C12(g) → CCI.(g) + 4 HCl(g) HCI CCl4 CH4 Cl2...
##### The frame is made from uniform rod which has a mass p per unit length. A...
The frame is made from uniform rod which has a mass p per unit length. A smooth recesser constrains the small rollers at A and B to travel horizontally. Force P is applied to the frame through a cable attached to an adjustable colla Determine the magnitudes and directions of the normal forces which ...
##### 1. A fair coin is tossed three times. Let A be the event that there are...
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment.  b. What are the sample space and probability funct...