Exam 1 Review
Here are some things to be familiar with for the first exam.
1. Basic concepts
- what are predicates, individual constants, and logical connectives? What
are the constraints on predicates and constants (e.g. whether a constant can
name more than one object, whether an object can fail to have a name,
whether a predicate can be vague or ambiguous)? What is the arity of a
predicate? What is an atomic sentence?
- what is logical necessity? logical equivalence? logical consequence?
logical validity? How are logical necessity, equivalence, and consequence related to
tautology, tautological equivalence, and tautological consequence?
- be able to identify sentences as tautologies, logical necessities,
Tarski's World necessities, or not necessary at all. (Remember, you can use
truth tables to determine whether a sentence is in the first category, and
you can determine whether a sentence is in the last category by seeing
whether you can construct a Tarski's world that makes it false.)
- logical equivalences: DeMorgan's laws, associativity, commutativity,
idempotence, double negation, distribution.
2. Truth Tables
- know truth tables for basic logical connectives, and know how to apply
them to construct truth tables for complex sentences.
- know how many rows a truth table must have; know how to construct the base
or reference columns (you need to follow the procedure used by our textbook;
it's just a convention, and other conventions are possible, but I need to be
able to evaluate your truth tables without spending a lot of time figuring
out which convention you're using).
- know how to use truth tables to determine whether a sentence is a
tautology, whether two sentences are tautologically equivalent, and whether
one sentence is a tautological consequence of a set of other sentences.
- know how to translate sentences from English into symbolic notation. (The
English sentences will either use English equivalents of Tarski's World
predicates, which you should already know how to translate, or I will give
you a list of predicates you can use in the translation.)
- You should also know how to translate sentences from symbolic notation
into English, but it's not likely I will ask questions like this on the
- Good practice: make sure you can do the translation homework
exercises. (If you had trouble with any of them, go back and take another
- Make sure you know how to handle "neither . . . nor" sentences! Also keep
in mind that lots of English expressions should get translated as "and,"
including "but," "however," "nevertheless," etc.
- know how to do proofs using all the rules we have covered so far: =Intro,
=Elim, Reit, ∧Intro, ∧Elim,
∨Intro, ∨Elim, ¬Intro, ¬Elim, ⊥Intro,
- Proofs will resemble the ones you've done for homework. Good practice
would be to make sure you can construct proofs corresponding to the
DeMorgan's equivalences, and the other logical equivalences we have
discussed, for example the distribution equivalences and the association equivalences. Make sure you can do the homework proofs
we have done so far; it might also be helpful to do unassigned homework
Last update: February 11, 2013.
Curtis Brown | Symbolic Logic
Department | Trinity