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MATH 5375 Partial Differential Equations

tag 0 Download 3 Pages / 540 Words tag 02-11-2020


In the rst two problems, it is understood that E; L; H1 and H2 are a plane, a line, and the two half-planes given by PS-1. Use of the Ruler Postulate or Ruler Placement Theorem is not allowed; the proofs should instead use Theorems B-1 through B-5, which were based on them.

  •  Prove Theorem 4: H1contains at least two points. Hint: You may use the resut of Exercise 2, which was proven in the presentation. First, devise a strategy that you can justify using previous results and postulates, then devise a well-written argument based on that strategy.
  • Prove Theorem 8: If A and B are convex then so also is A B.
  • (Theorem 8: The interior of a triangle is (always) a convex set. Hint: Use the result of x4.1 # 7.
  • Of the three gures shown, two can be drawn without lifting your pencil or retracing a line segmentm while the third one cannot. Which two can be drawn in this manner? Try to reproduce each gure on your paper without lifting your pencil or retracing a segment. Is there an easier way of arriving at a conclusion?
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