The Marking Scheme for Midterm Questions #3 and 4:

#3) Total 20 points broken down into

(a) 5 points for using correct definition of logical consequences.
    You need to mention a structure M and an object assignment sigma you 
need.
    Then follow the BSD carefully!! DO NOT skip the steps!
    5 points for solid complete proof.
(b) 5 points for understanding that you need a particular structure that
    satisfies LHS but not the RHS. 5 points for such correct structure
    (counter example will do so). Any structures with flaws in them
    would not get credits. Any attempts to prove it without an 
counterexample
    did not get credits as the proof contained extra assumptions or simply
    stated the statement you have to prove in a different way!

#4) Total 20 points broken down into

    10 points for correctly generating variables and the other 10 points for
    correctly built terms, atomic formulae, and the general formulae.  Any
    deviations from the correct ones lose points!