Courses/Computer Science/CPSC 203/CPSC 203 Template/Lecture Template/Lecture 16
Contents
Housekeeping
Required Reading
Introduction
Last class introduced Boolean Logic, via a series of Truth Tables. In this lecture, we will look at the notion of VALID reasoning within Boolean Logic, via a series of examples.
At the End of this lecture you will have practiced:
- Deterrmining the Validity of an Inference via Truth Tables
- Recognizing certain forms of Inference (e.g. Modus ponens, Modus tollens)
- Understand that "Valdity" in logic, is purely a matter of the FORM an argument takes.
Glossary
- Valid Inference. Via the truth table method, a propositional inference is valid IF AND ONLY IF there is no possible case where the premises are all true and the conclusion is false.
- Modus ponens. "Affirming mode". A pattern of valid inference of the form: "If A, then B; A; Therefore B".
- Modus tollens. "Denying Mode". A pattern of valid inference of the form: "If A, then B; Not B; Therefore Not A".
- Law of Non-Contradiction. The idea a statement can't be both True and also Not True.
- Law of the Excluded Middle. The idea that every statement is True or False.
Concepts
The Glossary above is explained via a series of examples of translating sentences into propositions, and propositions into truth tables, and then determining the validity of a particular argument.
A few demonstrations of critical ideas are in the document below:
Summary
Text Readings
Resources
The primary resources for this lecture was:
- Ones & Zeros -- Understanding Boolean Algebra, Digital Circuits and the Logic of Sets. 1998. By John R. Gregg
- Introduction to Logic. 2002. By Harry J. Gensler.
Supplementary References are:
- Logic. A Very Short Introduction. 2000. By Graham Priest.
- Logic Made Easy. How to Know When Language Decieves You. 2004. By Deborah J. Bennett.
- Feynman Lectures on Computation. 1996. By Richard P. Feynman.
Homework
1. It turns out that the 'AND' operator, can actually be constructed using the "OR" and "NOT" operators. Using Truth Tables, demonstrate this.
2. It turns out that the 'OR' operator, can actually be constructed using the "AND" and "NOT" operators. Using Truth Tables, demonstrate this.
3. It turns out that the 'XOR' operator, can actually be constructed using "AND", "OR", "NOT" operators. Using Truth Tables, demonstrate this.
4. It turns out that the 'Implication' operator can actually be constructed using "AND", "OR" and "NOT" operators. Using Truth Tables, demonstrate this.
5. Look through a news-paper or magazine and find an example of Modus tollens.
6. Look through a news-paper or magazine and find an example of Modus ponens.
7. Look through a news-paper or magazine, and find an example of an invalid inference.
