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

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

View Full Document Right Arrow Icon
The Foundations: Logic and Proofs Chapter 1 , Part I: Propositional Logic
Background image of page 1

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

View Full DocumentRight Arrow Icon
Chapter Summary Propositional Logic The Language of Propositions Applications Logical Equivalences Predicate Logic The Language of Quantifiers Logical Equivalences Nested Quantifiers Proofs
Background image of page 2
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)
Background image of page 3

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

View Full DocumentRight Arrow Icon
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)
Background image of page 4
Propositional Logic Summary The Language of Propositions Connectives Truth Values Truth Tables Applications Translating English Sentences Logic Puzzles Logical Equivalences Important Equivalences
Background image of page 5

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

View Full DocumentRight Arrow Icon
Propositional Logic Section 1.1
Background image of page 6
Section Summary Propositions Connectives Negation Conjunction Disjunction Implication; contrapositive, inverse, converse Biconditional Truth Tables
Background image of page 7

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

View Full DocumentRight Arrow Icon
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.
Background image of page 8
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
Background image of page 9

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

View Full DocumentRight Arrow Icon
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
Background image of page 10
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
Background image of page 11

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

View Full DocumentRight Arrow Icon
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
Background image of page 12
The Connective Or in English In English “or” has two distinct meanings.
Background image of page 13

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

View Full DocumentRight Arrow Icon
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 64

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

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online