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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 n1. 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 n1 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 n1 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).

