Dr. Cleary's Math 360 S26 Homework Assignments:

• HW1, due Tues, Feb 3rd
  Consider the following axiom set.
  • Axiom 1. Every team plays at least two games.
  • Axiom 2. Every game has at least two teams.
  • Axiom 3. There exists at least one team.
  1. What are the undefined terms in this axiom set?
  2. Prove Theorem 1. There exists at least one game.
  3. What is the minimum number of games? Prove.
  4. Find two models that show that the statement "There are exactly two teams" is independent of the axioms.
  5. Find two models that show that the statement "Every team plays every other team" is independent of the axioms.
• HW2, due Tues, Feb 10th
  • Stahl, 1.2 #2: make precise statements of Euclid's propositions 5 to 9 using modern terminology and notation
  • Stahl, 1.2, #10: prove that the angle bisectors of a triangle are concurrent (meet in a single point.) Does this hold in neutral geometry as well?

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