Course Outline for Mathematics 12, Page 2

Chabot College

Fall 2010

Chabot College Fall 2010

Course Outline for Mathematics 12

INTRODUCTION TO LOGIC

Catalog Description:

12 – Introduction to Logic 3 units

Introduction to formal deductive logic with emphasis on developing the basic concepts of modern symbolic logic; includes deductive validity, relation of ordinary languages to symbolic logic, distinction between inductive and deductive arguments, relation of truth to validity, 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. 3hours.
[Typical contact hours: 52.5]

Prerequisite Skills:

None

Expected Outcomes for Students:

Upon completion of the course, the student should be able to:

1. define the terms of propositional logic, including proposition, formula of propositional logic, sentential connectives, deductive argument, premise and 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 propositional logic developed in this course;

3. determine the validity or invalidity of deductive arguments which can be stated in the formulas of propositional logic;

4. prove the validity or invalidity of an argument of propositional logic;

5. demonstrate the consistency or inconsistency of a set of premises;

6. 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;

7. prove the validity of arguments which can be represented in terms of universally general formulas of first order predicate logic, and involving only the rules Universal Instantiation and Universal Generalization.

Course Content:

1. Propositional logic

2. Notation of propositional logic

3. Validity and invalidity of deductive arguments

4. Proving validity by a variety of methods, including conditional proof and reductio ad absurdum

5. Truth tables

6. Inconsistency of an inconsistent set of premises

First order predicate logic

a. Universal and existential quantifiers

b. Symbolic notation

7. Rule of Universal Instantiation

8. Rule of Universal Generalization

Methods of Presentation:

Lectures and discussions

Assignments and Methods of Evaluating Student Progress:

1. Typical Assignments

a. Written homework assignments, e.g. Translate “not every smile is genuine” into the symbolic notation of first order predicate logic.

b. Oral presentations on topics related to logic, e.g. Logic and computers; Fuzzy logic; Fallacies of weak induction; Scientific reasoning; Causality and Mill’s methods

2. Methods of Evaluating Student Progress

a. Oral presentations

b. Quizzes, examinations, midterm

c. Final Examination

Textbook(s) (Typical):

A Concise Introduction to Logic 10th Edition, Patrick Hurley, Wadsworth Publishers, 2008

Special Student Materials:

None.

J.T. 2009Curriculum/Math12CourseOutline.doc

Revised: October, 4, 2009