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CSC 165           Homework Assignment 1 -- 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.  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/undefined/ambiguous notation

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


1.  [20 marks]

     +  2 marks for each statement

    Error Codes:

    _A_ assumption [-1 mark]:  unreasonable assumption (either explicit or
        implicit), or reasonable but invalid implicit assumption

    _T_ translation [-1 mark]:  translation error (independently of
        assumptions)

    Marker's Comments:
     -  many students wrote the converse of the statement in part (i)
     -  1/2 for getting the arguments of predicates backwards
     -  many students misinterpreted "\-/ x, S(x) => ..." to mean
        "if all students ..."


2.  [15 marks]

    For each statement:

    _R_ relationship [1 mark]:  correct relationship to original statement

    _T_ translation [2 marks]:  correct translation into symbolic notation,
        or correct justification

    Marker's Comments:
     -  2/3 for (d) for saying "equivalent" without saying "contrapositive"


3.  [15 marks]

    _I1_ interpretation [3 marks]:  correct interpretation for S_1
        (whether given explicitly or implicitly)

    _I2_ interpretation [4 marks]:  correct interpretation for S_2
        (whether given explicitly or implicitly)

    For each combination S_i with A_j:

    _A_ answer [1 mark]:  correct value (true/false), relative to
        interpretation (i.e., give the mark if the value makes sense given
        the interpretation, even if the interpretation is incorrect)

    _J_ justification [1 mark]:  reasonable justification, relative to
        interpretation

    Marker's Comments:  (none)


4.  [10 marks]

    _E_ explicit [1 mark]:  explicit sets A,B,C clearly given

    _S3_ [3 marks]:  S_3 is true for the sets given (1 mark)
        and this is justified properly (2 marks)

    _S4_ [3 marks]:  S_4 is false for the sets given (1 mark)
        and this is justified properly (2 marks)

    _M_ minimum [3 marks]:  sizes of A,B,C as small as possible
        (3 if |A|,|B| <= 2, |C| <= 1; 2 if |A|,|B| <= 3, |C| <= 2,
         1 if |A|,|B|,|C| are all finite; 0 if any are infinite)

    Marker's Comments:
     -  -1 for specifically stating empty sets are not possible
     -  if either S_3 was false or S_4 was true, no marks for _M_


5.  [20 marks]

    (a) [8 marks]

        _A_ answer [2 marks]:  correct answer (yes)

        _J_ justification [6 marks]:  good justification

        Marker's Comments:  (none)

    (b) [12 marks]

        _A_ answer [4 marks]:  correct answer (including who is guilty and
            who is innocent)

        _J_ justification [8 marks]:  good justification

        Marker's Comments:
         -  some students described how to determine whether there is a
            unique solution, without actually doing it -- they only got
            marks for justification