Chapter1p1 (1)

# Chapter1p1 (1) - The Foundations Logic and Proofs Chapter 1...

This preview shows pages 1–14. Sign up to view the full content.

The Foundations: Logic and Proofs Chapter 1 , Part I: Propositional Logic

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

View Full Document
Chapter Summary Propositional Logic The Language of Propositions Applications Logical Equivalences Predicate Logic The Language of Quantifiers Logical Equivalences Nested Quantifiers Proofs
Logic Puzzles An island has two kinds of inhabitants, knights , who always tell the truth, and knaves , who always lie. You go to the island and meet A and B. A says “B is a knight.” B says “The two of us are of opposite types.” Example : What are the types of A and B? Raymond Smullyan (Born 1919)

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

View Full Document
Logic Puzzles An island has two kinds of inhabitants, knights , who always tell the truth, and knaves , who always lie. You go to the island and meet A and B. A says “B is a knight.” B says “The two of us are of opposite types.” Analysis: Let p and q be the statements that A is a knight and B is a knight, respectively. So, then p represents the proposition that A is a knave a nd q that B is a knave. Raymond Smullyan (Born 1919)
Propositional Logic Summary The Language of Propositions Connectives Truth Values Truth Tables Applications Translating English Sentences Logic Puzzles Logical Equivalences Important Equivalences

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

View Full Document
Propositional Logic Section 1.1
Section Summary Propositions Connectives Negation Conjunction Disjunction Implication; contrapositive, inverse, converse Biconditional Truth Tables

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

View Full Document
Propositions A proposition is a declarative sentence that is either true or false. Examples of propositions: a) The Moon is made of green cheese. b) Trenton is the capital of New Jersey. c) Toronto is the capital of Canada. ) d 1 + 0 = 1 ) e 0 + 0 = 2 Examples that are not propositions.
Propositional Logic Constructing Propositions Propositional Variables: p , q, r , s , … true is denoted by T false is denoted by F . Compound Propositions; constructed from logical connectives and other propositions Negation ¬ Conjunction Disjunction

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

View Full Document
Compound Propositions: Negation The negation of a proposition p is denoted by ¬ and has this truth table: Example : If denotes “The earth is round.”, then ¬ denotes “The earth is not round.” ¬ T F F T
Conjunction The conjunction of propositions p and q is denoted by and has this truth table: Example : If denotes “I am at home.” and denotes “It is raining.” then denotes “I am at home and it T T T T F F F T F F F F

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

View Full Document
Disjunction The disjunction of propositions p and q is denoted by and has this truth table: Example : If denotes “I am at home.” and denotes “It is raining.” then denotes “I am at home or it is T T T T F T F T T F F F
The Connective Or in English In English “or” has two distinct meanings.

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.

{[ snackBarMessage ]}

### Page1 / 64

Chapter1p1 (1) - The Foundations Logic and Proofs Chapter 1...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online