The assignment for our class is different from that for Whiteley's in several respects. So go by this, not by his list of questions.

  1. 5.3.3 b.
    (I did not say this in class on 29 January, but a SYMLOG printout is preferable here.)
  2. 5.4.1 b.
    Note that this true-false statement has an understood "For ALL \alpha, ..." at the beginning of it. So, in line with my remarks in the posting to our discussion list a week or two ago, you must give a general argument for the truth of this statement if you say it is true, whereas if you say it is false, then a single specific counterexample is enough to support your claim of falsehood.
  3. 5.4.4 f.
    Give a SYMLOG printout of an SD-derivation that derives both \alpha and \not \alpha, for some wff \alpha of your choice.
  4. 5.4.5 d.
    Again, give a SYMLOG printout. And of course you will have to understand precisely the definition (in class and in the book) of "SD-inconsistent", and also the "Test for Derivability", before you even know what your printout should contain.... :-)
  5. 5.4.7 h. (yes, SYMLOG printout again)
  6. For each of the arguments in (a) through (b) below,

    (i) give an SD-derivation (SYMLOG printout) of the conclusion from the premise(s), and

    (ii) give an English argument that, as closely as possible, paraphrases the SD-der. you gave in (i). (Examples of what I mean here will be given in class.) It may be fair to say that what I do when I have to construct a derivation is to map out an English version of it first; I certainly think in English rather than in SD! :-)

     
    (a)      A -> B               (b) \not A v B          (c)         
         ----------------             ----------              ----------
         \not B -> \not A               A -> B                A v \not A