Marker's comments on Problem Set 1 (Cook)

In general students did well:  the average mark was 41.5/50.
However some students did poorly and should consider dropping
the course.

Questions 1 and 4 involved proofs by structural induction:
For Quest 1 the induction is on formulas, and for Quest 4 the
induction is on terms.  The majority of students did well on
these, but a significant minority did not understand structural
induction.
   In general, the induction step assumes the induction hypothesis
for *all* formulas (or terms) of length less than n, and proves
it for an arbitrary term of length n.  This proceeds by looking
at the definition of formula (or term), and considering each
of the ways of building a formula (or term) from smaller
formulas (or terms). 
   The mistakes made usually involved considering a formula, say,
of length n+1 and trying to see how it could have been built
from a formula of length n.  The leads to a complicated and
incorrect proof.
   See the solutions to PS1 posted on the course Web site.

Another frequent problem in question 1 was not distinuishing
between A=B (formulas A,B are syntactially =, symbol by symbol)
and A <=> B (A and B are semantically equivalent).
PLEASE honour this distinction (at least in this course).

Quest 2 (LK rules for implication:  almost everyone got this.)

Quest 3:  Equivalence of forms of compactness:  Most people did
well, but some arguments were confused.

Quest 5 (Independence of commutativity of + from P1,P2,P3,P4):
Most people did well.