Rules and Laws

# Rules and Laws - • Is it possible to reduce even further...

This preview shows pages 1–4. Sign up to view the full content.

Discussion #11 Chapter 1, Section 6.1-5 1/16 Main Rules of Inference A, B |= A  B Law of combination A  B |= B Law of simplification A  B |= A Variant of law of simplification A |= A  B Law of addition B |= A  B Variant of law of addition A, AB |= B Modus ponens B, AB |= A Modus tollens AB, BC |= AC Hypothetical syllogism A  B, A |= B Disjunctive syllogism A  B, B |= A Variant of disjunctive syllogism AB, AB |= B Law of cases AB |= AB Equivalence elimination AB |= BA Variant of equivalence elimination AB, BA |= AB Equivalence introduction A, A |= B Inconsistency law

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Discussion #9 Chapter 1, Section 4 2/16 Logical Equivalence Leading to Reductions We can reduce  and  to , , and  by: P  Q (P  Q)  (Q  P) P  Q P  Q We now only need , , and .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: • Is it possible to reduce even further? Discussion #10 Chapter 1, Section 5 3/19 Laws of , , and Excluded middle law Contradiction law P P T P P F Name Law Identity laws P F P P T P Domination laws P T T P F F Idempotent laws P P P P P P Double-negation law (P) P Discussion #10 Chapter 1, Section 5 4/19 Commutative laws P Q Q P P Q Q P Name Law Associative laws (P Q) R P (Q R) (P Q) R P (Q R) Distributive laws (P Q) (P R) P (Q R) (P Q) (P R) P (Q R) De Morgan’s laws (P Q) P Q (P Q) P Q Absorption laws P (P Q) P P (P Q) P...
View Full Document

## This note was uploaded on 03/02/2012 for the course C S 236 taught by Professor Michaelgoodrich during the Winter '12 term at BYU.

### Page1 / 4

Rules and Laws - • Is it possible to reduce even further...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online