So what should you know for the test? Here is an indication (watch also on this web page for samples of class tests given in the past in this course):

- You should have a thorough mastery of truth tables. Know the definitions of the connectives "in your sleep". (And of course use the Symlog symbols for them, not the symbols used in some other course.) Know what the "standard ordering" for tva's is (Ganong also called it the lexicographic order), and use ONLY that ordering if you are asked to produce any truth tables, or if a truth table is necessary to justify something you claim in one of your test answers.
- Be able to USE the definitions of any of the terms we have defined in the course, and also able to WRITE DOWN clear and complete definitions of any of those terms. You should be able to define, and to use the definitions of, phrases such as: "\alpha entails \beta", "SL set", "\Gamma entails \beta", "\tau satisfies \beta", "\alpha is satisfiable", "\Gamma is satisfiable/consistent", "contradiction", "contingent wff", "tautology", "\alpha is logically equivalent to \delta", "inconsistent set", "premise/conclusion", "antecedent/consequent", "valid/invalid argument", "SD (or SD+) -valid argument", "SD-inconsistent set", "... is SD (or SD+) -derivable from ...", "... is an SD (SD+) -theorem of ...", "... is SD (or SD+) -equivalent to ...".
- Be able to state and able to use both the "test for entailment"
(p. 111) and the "test for SD (or SD+) -derivability", each of which
involves checking whether a certain set is inconsistent in a certain
sense, and each of which is sometimes the easiest way to approach a
question .
But do not go overboard and try to settle
**any**question about entailment or derivability by running to these "tests" -- after all, before we had the tests, we had definitions of entailment etc., which are often just as easy to apply as the tests, and sometimes easier. (Of course, also understand why these tests "make sense" -- we proved in class that the tests do in fact achieve what they claim to achieve.) - Know all the synonyms we have encountered (e.g. "contingent" = "truth-functionally indeterminate", "entails" = "logically implies", etc.). You may be given test questions involving one of the synonyms, and if you ask Ganong during the test whether a certain phrase means the same thing as another phrase, his answer will probably be, "You are supposed to know the answer to that." And he will not be happy that you asked. Know that the same symbol may mean different things in different contexts (e.g., \tau |= \alpha, \Gamma |= \alpha), and of course know what all the symbols mean -- |---- , for example (with an "SD" or "SD+" written under it, hard for me to typeset in html).
- Be comfortable with proof by cases and proof by contradiction
(this is what Ganong called these neato cool types of proof in SD,
SD+), and
*understand in your soul*why they work, why it is altogether fitting and proper that they are legitimate methods of proof. Be comfortable with the notion that inconsistent sets entail all wff's, and with the whole notion of the empty set, and able to check with care, but with ease, statements made about the empty set. (E.g., "Every element of the empty set is purple and has seven toes.") Believe Ganong when he says that every time he has played Bobby Fischer in a tournament chess game, he has checkmated BF in under twenty moves; be skeptical when he claims to have beaten BF even once in a tournament game. - Know exactly what the Soundness and Completeness theorems say, and be able to write them down if asked, and able to use them to solve problems and to justify answers you give.
- Of course, the more precisely you can write test answers, the
more specific you can be with counterexamples, etc., the better will
be your test result. Do not give the markers any chance to
misunderstand you (if you
*do*, they*will*). By the way, the people who have been giving the tutorials and marking the assignments so far, M. Rabus and J. Zhou, are**both former instructors**of Math 2090, and probably understand logic much better than Ganong does. (Rabus even taught 2090 before Ganong did.) Your tests will be marked in part by your instructor, and partly by Rabus and/or Zhou.

Ask again * in public, DURING class, NOT in private *,
on Friday, 14 February, for updates to this test
preparation file.