Chapter Nine:
PL with Identity
This chapter contains a presentation of first order logic with identity. We introduce the special 2-place predicate constant "I" (for identity) along with its semantics and rules for its use in derivations. Also we will begin the study of complex names, also known as "functions". (But, really, they won't be a problem for you if you've gotten this far!) The chapter concludes with a simple example from abstract algebra.
Also, more mundanely, symbolization exercises allow more sophisticated quantification. For example, with identity one may symbolize, "there are exactly two green marbles" rather than just "there is at least one green marble".
Start with the introductory tutorials presented below, then print out the reference manual for this chapter (that way you'll have a concise statement of this chapter's details to refer to even when away from the computer.) Finally, and most importantly, carefully work your way through the chapter exercises.
Tutorials for Chapter Nine
 1. |
An Introduction to Identity and Symbolization |
| 2. |
Predicate Logic with Identity: Syntax, Semantics, Derivation |
| 3. |
Complex Names (a.k.a. "functions") |
| 4. |
Very Elementary Abstract Algebra |
9.1ex
I Multiple Choice
9.1ex
II Symbolization with Identity
9.1ex
III More Symbolizations with Identity
9.2ex
I Derivations in PDI
Selected Answers
9.3ex
I Multiple Choice
9.4ex
I Group Theory Proofs
Chapter 9: Statement of the exercises.