MATH 363 Discrete Mathematics

email:zl zli2 com

 // home

 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).

Website design modified from Sliqua taken from OSWD