MATH 363 Discrete Mathematics

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Here are some explanation for shorthand used for marking the midterm and some remarks.
  • NAeq - "Not answered" equivalent. I would prefer if "Not answered" was written but other forms were accepted.
  • PT - Proved true. Assumed the conclusion and arrived at true (see common mistakes in proofs)
  • UI - "Upwards" induction. For question 7, adding a vertex to a tree rather than removing a vertex. See common mistakes in proofs. The proof would require also showing that all trees can be built by adding one vertex at a time.
  • Proved Q implies P rather than P implies Q. See updated common mistakes in proofs.
  • A variant of the previous error involves proving that some statement is true for n implies the same statement is true for n-1. There is nothing wrong in proving this except that it does not help complete a proof by induction. Induction works because we've proven a statement for some base case (e.g., n=1) and then we need to prove if the statement is true for n-1 implies the same statement is true for n. Applying the latter with n=2 gives us the statement for n=2. After this, applying the latter with n=2 gives us the statement for n=3. And so on.
    Proving that some statement is true for n implies the same statement is true for n-1 only shows that for any value less or equal to the base case, the statement is true (which is usually not many cases).
  • For question 6, some rather vague arguments about why d must appear twice were accepted. A more formal answer would have been preferred. Many errors are made assuming that something "must" happen.
  • The midterm is marked out of 33 instead of the originally intended 37. The maximum possible score was 40. As a consequence, many students got more than 100% (and they do get to keep the extra points).

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