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CSC 165            Homework Exercise 3 -- Marking Scheme        Winter 2009
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NOTE TO STUDENTS:

You will find below the marking scheme used for your homework, including
the meaning of marking codes and number of marks associated with each one.
This file also contains my instructions to the marker (so you can get an
idea of how the homework was marked) and the marker's comments about each
question.

Please take the time to read this carefully before you ask questions about
the grading of your homework.


NOTE TO MARKER:

Be picky!  On any homework, it is the responsibility of students to show
that they understand how to solve each problem and to write up their
answers carefully.  At the same time, keep in mind that exercises are worth
only 2% of the final grade, so your marking should be somewhat coarse.  And
remember that marking is not only about evaluating a student's performance,
but also mostly about giving them feedback so that they can learn from
their mistakes.  This is especially important for students who made
numerous or more serious mistakes, as they are likely to need more feedback
in order to understand why their answers were incorrect.

For each question, I list solution elements with an associated code for
writing on student papers (the letter(s) between underscores _) and a
number of marks.  There are also general errors (with associated codes)
given below, with a maximum number of marks to take off for each type of
general error (as a percentage of the value of the question).  You will
likely encounter other common errors, or maybe decide to break down the
marking scheme further.  Simply make note of these changes/additions to
the marking scheme, and introduce new code letters (or short words) to
allow you to quickly give accurate feedback to the students (both in terms
of what they did wrong and how many marks it cost them).  Your marking
comments will be included in this marking scheme and posted on the course
website so that students may look up the meaning of marking codes and
understand how their work was marked.


GENERAL ERRORS (marked negatively, in addition to any other errors):

    _N_ notation [up to 20%]:  incorrect/ambiguous notation

    _V_ vagueness [up to 20%]:  incorrect/unjustified/vague claim


1.  [15 marks]

    For each part:

    _A_ answer [1 mark]:  clear attempt to correctly prove or disprove

    _P_ proof [4 marks]:  correct sequence of equivalences (including brief
        justifications of each step) OR correct truth table (with rows
        showing inequivalence clearly identified)

    Expected Errors:

    _T_ truth table [at least -1 mark for _A_ and -2 marks for _P_]:
        giving a truth table to justify an equivalence OR
        giving only one assignment of values that makes the equivalence
        false (rather than the entire truth table)

    Additional Marking Codes:

    _M_ missing necessary steps for the proof [at least -1 mark for _P_]

    _X_ incorrect derivation [at least -1 mark for _P_]

    _I_ incomplete proof [at least -1 mark for _P_]

    _TI_ incomplete truth table [at least -1 mark for _P_]


2.  [5 marks]

    _L_ layout [1 mark]:  correct use of indentation

    _Q_ quantifiers [2 marks]:  correct structures for quantifiers
        (with clear assumptions, where appropriate, and conclusions)

    _C_ connectives [2 marks]:  correct structures for connectives
        (with clear assumptions, where appropriate, and conclusions)

    Expected Errors:

    _N_ negation [at least -2 marks]:  proof structure given for the
        original epsilon-delta statement (i.e., the negation of the
        statement on the exercise handout)

    Additional Marking Codes:

    _A_ incorrect assumption ("assume that 0 < |x-a| < d")
        [at least -1 mark]