cos 150 discrete structures assoc. prof. svetla boytcheva fall semester 2014
TRANSCRIPT
Code of Ethics
All course materials are adapted version of the textbook: Susanna S. Epp, Discrete Mathematics with Applications, Fourth Edition, Cengage Learning.
Some images – McGrawHill For materials from other sources, please see the
copyright reverence below each slide.
04/19/23
Use of Logic
Propositional Logic First Order Logic (Quantifiers)/ Predicate Logic Boolean Algebra
04/19/23
Outline
Logical Form and Logical Equivalence Statements; Compound Statements; Truth Values;
Evaluating the Truth of More General Compound Statements; Logical Equivalence; Tautologies
and Contradictions; Summary of Logical Equivalences
Conditional Statements Logical Equivalences Involving →; Representation of If-Then As Or; The Negation of a Conditional Statement; The Contrapositive of a Conditional Statement; The Converse and Inverse of a Conditional Statement; Only If and
the Biconditional; Necessary and Sufficient Conditions;
Valid and Invalid Arguments Modus Ponens and Modus Tollens; Additional Valid Argument Forms: Rules of Inference;
Use of Logic
In mathematicsGive a precise meaning of statementsDistinguish between valid and invalid argumentsProvide use of “correct” reasoning
Natural language can be very ambiguousHe ate the cookies on the couchThis is a good soupYou could do with a new automobile. How about a
test drive?
04/19/23
Use of Logic
Natural language can be very ambiguousThis is a good soupYou could do with a new automobile. How about a
test drive? I shot an elephant in my pajamas.
04/19/23
Use of Logic
In computingDesign new data/knowledge from existing factDesign of computer circuitsConstruction of computer programsVerification of correctness of programs and circuit
designSpecification
04/19/23
Statements (propositions)
Propositional logic deals with statements and their truth value
Truth values are TRUE (T or 1) and FALSE (F or 0)
04/19/23
Example Statements
1+1= 2 (statement, T) The moon is made of cheese (statement, F) Go home! (no statement, imperative) What a beautiful garden (no statement,
exclamation) Alice said: “What a beautiful garden ” (statement,
depends on Alice) Y+1=2 (no statement, uncertain)
04/19/23
Translating from English to Symbols: But and Neither-Nor
“Jim is tall but he is not heavy.” Shakespeare: “Neither a borrower nor a lender be”
04/19/23
Truth Table of negation
Unary connective
p: “Today is Wednesday”p: “Today is not Wednesday”
04/19/23
Binary connective
Example p: “Today is Wednesday” q: “It is raining”p q: “Today is Wednesday and it is raining”
Truth Table of conjunction
04/19/23
Truth Table of disjunction
04/19/23
Binary connective
Example p: “Today is Friday” q: “Today is Saturday”p q: “Today is Friday or Saturday”
Binary connective
Example pq “You can follow the rules or be disqualified”
Truth Table of exclusive or
04/19/23
Truth Table of implication
Binary connective
Example p -> q: “If black is white, then we live in Antarctica”
04/19/23