CSE 311 Foundations of Computing I Autumn 2011 Lecture 1 Propositional Logic.

Slides:



Advertisements
Similar presentations
Propositional Equivalences
Advertisements

Af2 Introduction. What’s the course about? Discrete Mathematics The mathematics that underpins computer science and other sciences as well.
Grading Lecture attendance: -1% per 2 unexcused absences
1. Propositions A proposition is a declarative sentence that is either true or false. Examples of propositions: The Moon is made of green cheese. Trenton.
CSE 311 Foundations of Computing I Spring 2013 Lecture 1 Propositional Logic.
Syllabus Every Week: 2 Hourly Exams +Final - as noted on Syllabus
1 Section 1.1 Logic. 2 Proposition Statement that is either true or false –can’t be both –in English, must contain a form of “to be” Examples: –Cate Sheller.
CSE 321 Discrete Structures Winter 2008 Lecture 1 Propositional Logic.
CSE115/ENGR160 Discrete Mathematics 01/17/12 Ming-Hsuan Yang UC Merced 1.
First Order Logic. Propositional Logic A proposition is a declarative sentence (a sentence that declares a fact) that is either true or false, but not.
CSE 311 Foundations of Computing I Autumn 2011 Lecture 2 More Propositional Logic Application: Circuits Propositional Equivalence.
The Foundations: Logic and Proofs
1 Math/CSE 1019C: Discrete Mathematics for Computer Science Fall 2011 Suprakash Datta Office: CSEB 3043 Phone: ext
Discrete Mathematics Goals of a Discrete Mathematics Learn how to think mathematically 1. Mathematical Reasoning Foundation for discussions of methods.
CSE 311 Foundations of Computing I Autumn 2012 Lecture 1 Propositional Logic 1.
Discrete Mathematics and Its Applications
COS 150 Discrete Structures Assoc. Prof. Svetla Boytcheva Fall semester 2014.
© by Kenneth H. Rosen, Discrete Mathematics & its Applications, Sixth Edition, Mc Graw-Hill, 2007 Ch.1 (Part 1): The Foundations: Logic and Proofs Introduction.
CS 285- Discrete Mathematics Lecture 2. Section 1.1 Propositional Logic Propositions Conditional Statements Truth Tables of Compound Propositions Translating.
Chapter 1: The Foundations: Logic and Proofs
CISC 2315 Discrete Structures Professor William G. Tanner, Jr. Fall 2010 Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability,
Foundations of Computing I CSE 311 Fall CSE 311: Foundations of Computing I Fall 2014 Lecture 1: Propositional Logic.
CSci 2011 Textbook ^Discrete Mathematics and Its Applications,  Rosen  6th Edition  McGraw Hill  2006.
Discrete Mathematics Lecture1 Miss.Amal Alshardy.
Discrete Structures – CS Text Discrete Mathematics and Its Applications Kenneth H. Rosen (7 th Edition) Chapter 1 The Foundations: Logic and Proofs.
Lecture 4. CONDITIONAL STATEMENTS: Consider the statement: "If you earn an A in Math, then I'll buy you a computer." This statement is made up of two.
1 CMSC 250 Discrete Structures CMSC 250 Lecture 1.
SSK3003 DISCRETE STRUCTURES
LOGIC Lesson 2.1. What is an on-the-spot Quiz  This quiz is defined by me.  While I’m having my lectures, you have to be alert.  Because there are.
September1999 CMSC 203 / 0201 Fall 2002 Week #1 – 28/30 August 2002 Prof. Marie desJardins.
1/10/ Math/CSE 1019N: Discrete Mathematics for Computer Science Winter 2007 Suprakash Datta Office: CSEB 3043 Phone:
Chapter 1: The Foundations: Logic and Proofs
Section 1.1. Section Summary Propositions Connectives Negation Conjunction Disjunction Implication; contrapositive, inverse, converse Biconditional Truth.
UMBC CMSC 203, Section Fall CMSC 203, Section 0401 Discrete Structures Fall 2004 Matt Gaston
Mathematics for Comter I Lecture 2: Logic (1) Basic definitions Logical operators Translating English sentences.
رياضيات متقطعة لعلوم الحاسب MATH 226. Text books: (Discrete Mathematics and its applications) Kenneth H. Rosen, seventh Edition, 2012, McGraw- Hill.
Discrete Structures Class Meeting 1. Outline of Today Information sheet Questionnaire Quiz 0 Learning mathematics – Reading math – Solving problems.
Section 1.1. Propositions A proposition is a declarative sentence that is either true or false. Examples of propositions: a) The Moon is made of green.
Discrete Mathematics Lecture # 4. Conditional Statements or Implication  If p and q are statement variables, the conditional of q by p is “If p then.
1 Georgia Tech, IIC, GVU, 2006 MAGIC Lab Rossignac Lecture 01: Boolean Logic Sections 1.1 and 1.2 Jarek Rossignac.
CSE 311: Foundations of Computing Fall 2013 Lecture 1: Propositional logic.
Logical Operators (Connectives) We will examine the following logical operators: Negation (NOT,  ) Negation (NOT,  ) Conjunction (AND,  ) Conjunction.
Simple Logic.
Discrete Structures for Computer Science Presented By: Andrew F. Conn Slides adapted from: Adam J. Lee Lecture #1: Introduction, Propositional Logic August.
Discrete Mathematical
Niu Kun Discrete Mathematics Chapter 1 The Foundations: Logic and Proof, Sets, and Functions Niu Kun 离散数学.
6/20/2018 Arab Open University Faculty of Computer Studies M131 - Discrete Mathematics 6/20/2018.
Logic.
Citra Noviyasari, S.Si, MT
MATH 245 Spring 2009 This is mathematics for computer science
CSE 311 Foundations of Computing I
COT 3100, Spr Applications of Discrete Structures
(CSC 102) Discrete Structures Lecture 2.
CPCS222 Discrete Structures I
Ch.1 (Part 1): The Foundations: Logic and Proofs
CSS 342 Data Structures, Algorithms, and Discrete Mathematics I
The Foundations: Logic and Proofs
Principles of Computing – UFCFA3-30-1
CSCI 3310 Mathematical Foundation of Computer Science
CSE 311 Foundations of Computing I
CSE 311 Foundations of Computing I
Discrete Mathematics and Its Applications Kenneth H
Discrete Mathematics Lecture 2: Propositional Logic
CSE 321 Discrete Structures
CSE 321 Discrete Structures
MAT 3100 Introduction to Proof
Discrete Mathematics Lecture 2: Propositional Logic
Cs Discrete Mathematics
Discrete Structures Prepositional Logic 2
The Foundations: Logic and Proofs
Presentation transcript:

CSE 311 Foundations of Computing I Autumn 2011 Lecture 1 Propositional Logic

About the course From the CSE catalog: –CSE 311 Foundations of Computing I (4) Examines fundamentals of logic, set theory, induction, and algebraic structures with applications to computing; finite state machines; and limits of computability. Prerequisite: CSE 143; either MATH 126 or MATH 136. What I think the course is about: –Foundational structures for the practice of computer science and engineering

Why this material is important Language and formalism for expressing ideas in computing Fundamental tasks in computing –Translating imprecise specification into a working system –Getting the details right

Topic List Logic/boolean algebra: hardware design, testing, artificial intelligence, software engineering Mathematical reasoning/induction: algorithm design, programming languages Number theory: cryptography, security, algorithm design Relations/relational algebra: databases Finite state machines: Hardware and software design, automatic verification Turing machines: Halting problem

Administration Instructors –Richard Anderson –Paul Beame Teaching Assistants –Eric Wu, Kristin Weber, Ben Birnbaum, Patrick Williams Quiz sections –Thursday Text: Rosen, Discrete Mathematics –7 th Edition –6 th Edition –5 th Edition Homework –Due Wednesdays Exams –Midterm, Friday, Nov 4 –Final, Monday, Dec 12, 2:30-4:20 pm or 4:30-6:20 This is the original time for the A section All course information posted on the web Sign up for the course mailing list

Propositional Logic

Propositions A statement that has a truth value Which of the following are propositions? –The Washington State flag is red –It snowed in Whistler, BC on January 4, –Rick Perry won the Iowa straw poll –Space aliens landed in Roswell, New Mexico –Turn your homework in on Wednesday –Why are we taking this class? –If n is an integer greater than two, then the equation a n + b n = c n has no solutions in non-zero integers a, b, and c. –Every even integer greater than two can be written as the sum of two primes –This statement is false –Propositional variables: p, q, r, s,... –Truth values: T for true, F for false

Compound Propositions Negation (not)  p Conjunction (and) p  q Disjunction (or)p  q Exclusive orp  q Implicationp  q Biconditionalp  q

Truth Tables p  p p pq p  q pq p  q pq p  q x-or example: “you may have soup or salad with your entree”

Understanding complex propositions Either Harry finds the locket and Ron breaks his wand or Fred will not open a joke shop Atomic propositions h: Harry finds the locket r: Ron breaks his wand f: Fred opens a joke shop (h  r)  f

Understanding complex propositions with a truth table h r f h  r  f f (h  r)   f

Aside: Number of binary operators How many different binary operators are there on atomic propositions?

p  qp  q Implication –p implies q –whenever p is true q must be true –if p then q –q if p –p is sufficient for q –p only if q pq p  q

If pigs can whistle then horses can fly

Converse, Contrapositive, Inverse Implication: p  q Converse: q  p Contrapositive:  q   p Inverse:  p   q Are these the same? Example p: “x is divisible by 2” q: “x is divisible by 4”

Biconditional p  q p iff q p is equivalent to q p implies q and q implies p pq p  q

English and Logic You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old –q: you can ride the roller coaster –r: you are under 4 feet tall –s: you are older than 16 ( r   s)   q