What to study for Test 1
Test 1 will be a bit of a push-over provided you've done the readings
and assignments. I will ask you to give some definitions, so you should
know the meaning of "proposition", "deductive propositional logic",
"valid argument", "sound argument", "tautology", "contradiction",
"contingency", "truth functional connective", "truth functional
equivalence", (and maybe one or two others, like "inclusive or",
"exclusive or", "material implication", ...)
You should be able to construct truth tables for propositions, determine
if a "word" made up of logical symbols is a well formed formula (WFF),
translate sentences to and from the notation of propositional logic, and
recognise if one proposition is a substitution instance of another.
You should be able to solve knights & knaves problems, and explain
the process used to arrive at your solution. You should understand the
simple principles underlying several types of such problems, as set out
in the text.
You should be able to recognise simple formal deductive
arguments as valid or not.
I may remind you of other matters in class - the bottom line is: you are
responsible for the material of Chapters 1 and 2 from the text, as well as
the notes from class.
Example Test "Template"
(You should look at the practice test itself to see how this is presented!)
- Give brief definitions (a sentence or two at most!) of the
Some terms will be chosen for this problem from the text.
- Construct truth tables for the following propositions. In each
case, state whether the proposition is a tautology, a contradiction, or
Some formulas will be chosen for this problem.
You'll have to construct their truth tables. Deciding whether the
formula is then a tautology, contradiction, or contingency should be
easy once the table is constructed (correctly!).
- [Some "quickies"; you only need to give a one-word answer, no
justifications are required:]
- For each of the following, state whether it is a well formed
formula or not.
Some expressions, some WFFs, some not, will be chosen for this problem.
For this problem, strict attention to brackets is necessary - I do not
intend to include "short-cuts" - although I won't give you "trick
examples", like A B → C,
which isn't strictly a WFF, since according to the definition, one needs
brackets (A B) → C.
- For each of the following pairs, state whether the first formula
is a substitution instance of the second.
Some pairs of expressions will be chosen for this problem.
There is a similar exercise in the text Ex 1.3.8.
- Translate the following English sentences into propositional formulas
(WFFs), using appropriate abbreviations.
- Translate the following WFFs into English sentences.
These exercises are like the homework problems - you don't have to
justify your answers, but they must be correct(!).
- The following problems are situated on "The island of Knights and
each individual is either a knight (who always tells the
truth) or a knave (who always lies).
Please give some justification for
your answers; e.g. if you consider cases, list each case and what its
consequences are, with your reasons.
Some sample problems, like the ones in Ex 1.5.1, will be
chosen for this problem. The justifications I am looking for are simple
ones like those given in class.
- The following diagram is intended to give a format for a valid
argument; does it succeed? (I.e. is the argument format in fact
valid?) Justify your answer by indicating what valid steps are used at
each point, or which step (or steps) are in fact not valid.
I will give a proof-tree diagram like the ones at the end of
Chapter 2; your task is to determine if
it follows the "rules" which guarantee it's valid.
- There will also be a brief "essay question", just to see if
you're thinking about what we've discussed, and can express yourself
coherently. (About a page, max.)