Chabot College/Las Positas College
January 1994
Course Outline for Mathematics 12A
LOGIC I
Catalog Description:
12A - Logic I
3 units
Introduction to formal deductive logic with emphasis on developing the basic concepts of modern
symbolic logic; includes the concept of deductive validity, relation of ordinary languages to symbolic
logic, distinction between inductive validity and deductive logic, relation of truth to validity and the
uses of truth tables, role of logic in the disciplines of mathematics, philosophy and sciences, rules of
inference for propositional logic and first order predicate logic. 3 hours.
Expected Outcomes for Students:
Upon completion of the course, the student should be able to:
1.
operationally define the technical terms of sentential (propositional) logic, including such
terms as: proposition, formula of sentential logic, sentential connectives, deductive
argument, premise of an argument, conclusion of an argument, validity, invalidity,
consistency, inconsistency, disjunction, conjunction, conditional (implication) bi-conditional
(equivalence), and negation;
2.
translate propositions stated in ordinary language into logic formulas, using the notation of
sentential logic developed in this course;
3.
determine the validity or invalidity of deductive arguments which can be stated in the
formulae of sentential logic;
4.
determine the consistency or inconsistency of a given set of premises which are able to be
represented in the formulae of sentential logic;
5.
prove the validity of a valid argument of the sentential logic, using the rules of validity
developed in this course, and including the rules: tautological implication, substitution,
conditional proof, and reductio ad absurdum;
6.
prove the invalidity of an invalid argument of sentential logic, using the method of assigning
truth values;
7.
demonstrate the consistency of a consistent set of premises using the method of assigning
truth values;
8.
demonstrate the inconsistency of an inconsistent set of premises, using the method of
reductio ad absurdum;
9.
translate ordinary language propositions into the notation of the first order predicate logic
using universal and existential quantifiers, and the symbolic notation developed in this
course;
10.
prove the logical validity of arguments which can be represented in terms of universally
general formulae of first order predicate logic, and involving only the rules Universal
Specification and Universal Generalization.
Course Content:
The course will include the following topics:
1.
Sentential (propositional) logic
2.
Notation of sentential logic
3.
Validity and invalidity of deductive arguments
4.
Rules of validity
a.
tautological implication
b.
substitution
c.
conditional proof
5.
6.
7.
8.
9.
d.
reductio ad absurdum
Truth values
Inconsistency of an inconsistent set of premises
First order predicate logic
a.
Universal and existential quantifiers
b.
Symbolic notation
Rule of Universal Specification
Rule of Universal Generalization
Methods of Presentation:
1.
Lectures/discussions.
2.
Students will work representative logic problems.
Methods of Evaluating Student Progress:
1.
Homework
2.
Quizzes
3.
Final examinations
Textbook(s) (Typical):
A Concise Introduction to Logic, Patrick Hurley, Wadsworth Publishers
Special Student Materials:
dm/hps revised 1/94
a:MA13CO.CON
None.