MAA 3200 – INTROD TO ADV MATH FLORIDA INT'L UNIV.
Review for Test #1 (Sept. 30th)                                   FALL  2008

REMEMBER TO BRING AN 8’’x11” BLUE EXAM BOOKLET FOR THE TEST

       KEY CONCEPTS AND MAIN DEFINITIONS:

Propositional logic, basic propositions, logical connectives, (complex) propositions,

tautology, logically equivalent propositions, logically implies, Predicate logic, quantifiers,

formulas of predicate logic, logically valid formulas, Theory of sets; intersection, union

and relative complements of sets; symmetric difference of two sets, subset, power set,

families and indexed families of sets, union and intersection of indexed families of sets,

proof strategies, proof by contradiction, counter-examples, ordered pairs, Cartesian

product of two sets, relations, range and domain of a relation, inverse and compositions

of relations; reflexive, symmetric, anti-symmetric, transitive, and circular relations;
       equivalence relations R on A, equivalence classes of R, A modulo R, partitions of A.
       Functions as special relations: domain, range, and codomains of functions.  Injective
       (one-to-one), surjective (onto), and bijective(one-to-one & onto) functions.


MAIN PROBLEM SOLVING TECHNIQUES:

1. Determining if the complex proposition A is logically equivalent to the complex

proposition B or if A logically implies B by using truth tables in Propositional Logic.

2. Translating English statements into formulas of Propositional Logic. Determining

if an argument is logically valid.

3. Translating English statements into formulas of Predicate Logic. Determining if

one formula of predicate logic is logically equivalent to another.

4. Proving that certain identities and subsets relation involving sets are true by using

logic; or proving they are false by using counter-examples.

5. Proving certain identities involving the Cartesian products and proving results about

certain properties of relations.

       6. Proving that a given relation R on A is an equivalence relation and finding the equi-
             valence classes into which A is partitioned by R.

7. Finding domains and ranges of functions and proving facts about functions and com-
             positions of functions.
8. Proving if a function is injective, surjective, bijective, or none of these.