There are seven standing committees on the t lying Aviators Club. In drawing up a set of by-laws for committee membership, the members wanted to maximize both die distribution of its members serving on committees, and communication between ) committees. They decided to adopt the following rules:
(1) There shall be seven committees of the Flying Aviators Club, including the Executive, Program, and Nominating Committees. The other committees shall be designated A, B, C, and D.
(2) The Executive Committee consists of just the President, Vice-President, and Secretary/Treasurer.
(3) The President shall serve on the three named committees mentioned in Rule 1.
(4) Each member-at-large of the Flying Aviators Club must serve on at least three committees.
(5) Two or more members are prohibited from belonging to the same two commit-tees.
(6) Each two committees must have a member in common.
Show that the members have unwittingly adopted a list of rules (hat will work only if the club has precisely seven members. (Hint: Use "points" for members and let "lines" represent committees.)
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