Introduction to Symbolic Logic

Slides:

Advertisements

Similar presentations

Geometry Logic.

Advertisements

TRUTH TABLES Section 1.3.

TRUTH TABLES The general truth tables for each of the connectives tell you the value of any possible statement for each of the connectives. Negation.

Constructing a Truth Table

Truth Tables Presented by: Tutorial Services The Math Center.

John Rosson Thursday February 15, 2007 Survey of Mathematical Ideas Math 100 Chapter 3, Logic.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 3.2 Truth Tables for Negation, Conjunction, and Disjunction.

2/17/2008Sultan Almuhammadi1 ICS Logic & Sets (An Overview) Week 1.

1 Math 306 Foundations of Mathematics I Math 306 Foundations of Mathematics I Goals of this class Introduction to important mathematical concepts Development.

Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley. All rights reserved.

Truth Tables for Negation, Conjunction, and Disjunction.

3.2 – Truth Tables and Equivalent Statements

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 3.2 Truth Tables for Negation, Conjunction, and Disjunction.

Splash Screen. Then/Now You found counterexamples for false conjectures. (Lesson 2–1) Determine truth values of negations, conjunctions, and disjunctions,

Propositional Logic.

Section 1-4 Logic Katelyn Donovan MAT 202 Dr. Marinas January 19, 2006.

Chapter 1 The Logic of Compound Statements. Section 1.1 Logical Form and Logical Equivalence.

BY: MISS FARAH ADIBAH ADNAN IMK. CHAPTER OUTLINE: PART III 1.3 ELEMENTARY LOGIC INTRODUCTION PROPOSITION COMPOUND STATEMENTS LOGICAL.

Logic Geometry Unit 11, Lesson 5 Mrs. Reed. Definition Statement – a sentence that is either true or false. Example: There are 30 desks in the room.

Logical Form and Logical Equivalence Lecture 2 Section 1.1 Fri, Jan 19, 2007.

Logic Disjunction A disjunction is a compound statement formed by combining two simple sentences using the word “OR”. A disjunction is true when at.

HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Section 3.2 Truth Tables.

3.3: Truth Tables. Types of Statements Negation: ~p Conjunction: p ˄ q (p and q) Disjunction: p V q (p or q, or both) Conditional: p → q (if p, then q)

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.

Chapter 3: Introduction to Logic. Logic Main goal: use logic to analyze arguments (claims) to see if they are valid or invalid. This is useful for math.

How do I show that two compound propositions are logically equivalent?

Review Given p: Today is Thursday q: Tomorrow is Friday

Truth Tables Geometry Unit 11, Lesson 6 Mrs. King.

Thinking Mathematically

Welcome to Interactive Chalkboard

Logical Form and Logical Equivalence Lecture 1 Section 1.1 Wed, Jan 12, 2005.

Lesson 20 INTERPRETING TRUTH TABLES. Review Conditional Statements (Less. 17) Original If p, then q. Converse If q, then p. Inverse If ~p, then ~q. Contrapositive.

Conditional Statements – Page 1CSCI 1900 – Discrete Structures CSCI 1900 Discrete Structures Conditional Statements Reading: Kolman, Section 2.2.

Logic Eric Hoffman Advanced Geometry PLHS Sept

TRUTH TABLES. Introduction The truth value of a statement is the classification as true or false which denoted by T or F. A truth table is a listing of.

Notes - Truth Tables fun, fun, and more fun!!!!. A compound statement is created by combining two or more statements, p and q.

UNIT 01 – LESSON 10 - LOGIC ESSENTIAL QUESTION HOW DO YOU USE LOGICAL REASONING TO PROVE STATEMENTS ARE TRUE? SCHOLARS WILL DETERMINE TRUTH VALUES OF NEGATIONS,

9.2 Compound Sentences Standard 5.0, 24.0 Standard 5.0, 24.0 Two Key Terms Two Key Terms.

Section 1.1 Propositions and Logical Operations. Introduction Remember that discrete is –the study of decision making in non-continuous systems. That.

TRUTH TABLES Edited from the original by: Mimi Opkins CECS 100 Fall 2011 Thanks for the ppt.

Lesson 2-2.B Logic: Truth Tables. 5-Minute Check on Lesson 2-2.A Transparency 2-2 Make a conjecture about the next item in the sequence. 1. 1, 4, 9, 16,

Review Find a counter example for the conjecture Given: JK = KL = LM = MJ Conjecture: JKLM forms a square.

 2012 Pearson Education, Inc. Slide Chapter 3 Introduction to Logic.

Ms. Andrejko 2-2 Logic. Real World Legally Blonde.

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

 Statement - sentence that can be proven true or false  Truth value – true or false  Statements are often represented using letters such as p and q.

Chapter 1 Logic and proofs

Section 3.2: Truth Tables for Negation, Conjunction, and Disjunction

Logical Operators (Connectives) We will examine the following logical operators: Negation (NOT,  ) Negation (NOT,  ) Conjunction (AND,  ) Conjunction.

Discrete Structures for Computer Science Presented By: Andrew F. Conn Slides adapted from: Adam J. Lee Lecture #1: Introduction, Propositional Logic August.

Introduction to Logic © 2008 Pearson Addison-Wesley.

Truth Tables for Negation, Conjunction, and Disjunction

Presented by: Tutorial Services The Math Center

Lesson 2-2 Logic A statement is a sentence that can either be true or false. The truth or falsity of a statement can be called its truth value. Compound.

Thinking Mathematically

Truth Tables and Equivalent Statements

CHAPTER 3 Logic.

Truth Tables for Negation, Conjunction, and Disjunction

Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.

Discrete Mathematics Lecture 2: Propositional Logic

Statements of Symbolic Logic

Section 3.7 Switching Circuits

And represent them using Venn Diagrams.

Section 3.2 Truth Tables for Negation, Conjunction, and Disjunction

CHAPTER 3 Logic.

2-2 Logic Vocab Statement: A sentence that is either true or false

CHAPTER 3 Logic.

Presentation transcript:

Introduction to Symbolic Logic 2-Ext Introduction to Symbolic Logic Lesson Presentation Holt Geometry

Objectives Analyze the truth value of conjunctions and disjunctions. Construct truth tables to determine the truth value of logical statements.

Vocabulary compound statement conjunction disjunction truth table

Symbolic logic is used by computer programmers, mathematicians, and philosophers to analyze the truth value of statements, independent of their actual meaning. A compound statement is created by combining two or more statements. Suppose p and q each represent a statement. Two compound statements can be formed by combining p and q: a conjunction and a disjunction.

A conjunction is true only when all of its parts are true A conjunction is true only when all of its parts are true. A disjunction is true if any one of its parts is true.

Example 1: Analyzing Truth Values of Conjunctions and Disjunctions Use p, q, and r to find the truth value of each compound statement. p: The month after April is May. q: The next prime number after 13 is 17. r: Half of 19 is 9. A. p  q Both p and q are true, therefore the disjunction is true. B. q  r Since r is false the conjunction is false.

Check It Out! Example 1 Use p, q, and r to find the truth value of each compound statement. p: Washington, D.C., is the capital of the United States. q: The day after Monday is Tuesday. r: California is the largest state in the United States. A. r  p Since p is true the disjunction is true. B. p  q Since both p and q are true the conjunction is true.

A table that lists all possible combinations of truth values for a statement is called a truth table. A truth table shows you the truth value of a compound statement, based on the possible truth values of its parts. p q p  q p  q p  q T F

Make sure you include all possible combinations of truth values for each piece of the compound statement. Caution The negation (~) of a statement has the opposite truth value. Remember!

Example 2: Constructing Truth Tables for Compound Statements Construct a truth table for the compound statement ~p  ~q. p q ~p ~q ~p  ~q T T F F F T F F T T F T T F T F F T T T

u v ~u ~v ~u  ~v T T F F F T F F T F F T T F F F F T T T Check It Out! Example 2 Construct a truth table for the compound statement ~u  ~v. u v ~u ~v ~u  ~v T T F F F T F F T F F T T F F F F T T T