Thinking Mathematically

Slides:

Advertisements

Similar presentations

Discrete Mathematics Lecture 1 Logic of Compound Statements

Advertisements

TRUTH TABLES Section 1.3.

Truth Tables How to Make and Use. Making a Truth Table To determine the number of rows other than the heading row. To determine the number of rows other.

Introduction to Symbolic Logic

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

CS128 – Discrete Mathematics for Computer Science

MAT 142 Lecture Video Series. Truth Tables Objectives Construct a truth table for a given symbolic expression. Determine if two given statements are.

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

Chapter 9: Boolean Algebra

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

Chapter 2: The Logic of Compound Statements 2.1 Logical Forms and Equivalence 12.1 Logical Forms and Equivalences Logic is a science of the necessary laws.

3.2 – Truth Tables and Equivalent Statements

Truth Tables (MAT 142) Truth Tables.

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

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 3.4 Equivalent Statements.

Copyright © Curt Hill Truth Tables A way to show Boolean Operations.

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.

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

Thinking Mathematically Logic 3.6 Negations of Conditional Statements and De Morgan’s Laws.

Thinking Mathematically Equivalent Statements, Conditional Statements, and De Morgan’s Laws.

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.

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

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

Thinking Mathematically

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.

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,

Symbolic Logic The Following slide were written using materials from the Book: The Following slide were written using materials from the Book: Discrete.

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

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.

Thinking Mathematically Logic 3.4 Truth Tables for the Conditional and Biconditional.

 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.

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

 Conjunctive Normal Form: A logic form must satisfy one of the following conditions 1) It must be a single variable (A) 2) It must be the negation of.

© 2010 Pearson Prentice Hall. All rights reserved. 1 §3.3, Truth Tables for Negation, Conjuction, and Disjunction.

Introduction to Logic © 2008 Pearson Addison-Wesley.

Truth Tables for Negation, Conjunction, and Disjunction

Presented by: Tutorial Services The Math Center

2. The Logic of Compound Statements Summary

The Foundations: Logic and Proofs

Truth Tables and Equivalent Statements

CHAPTER 3 Logic.

Truth Tables for Negation, Conjunction, and Disjunction

Classwork/Homework Classwork – Page 90 (11 – 49 odd)

(CSC 102) Discrete Structures Lecture 2.

Truth Tables for Negation, Conjunction, and Disjunction

Discrete Mathematics Lecture # 2.

The Lost Art of Argument

Propositional Equivalences

Information Technology Department

MAT 142 Lecture Video Series

Section 3.4 Equivalent Statements

TRUTH TABLES continued.

(1.4) An Introduction to Logic

Discrete Mathematics and Its Applications Kenneth H

Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.

Discrete Mathematics Lecture 2: Propositional Logic

Discrete Mathematics Lecture 2: Propositional Logic

Equivalent Statements

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

Section 3.4 Equivalent Statements

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

CHAPTER 3 Logic.

Presentation transcript:

Thinking Mathematically Truth Tables for Negation, Conjunction, and Disjunction

“Truth Tables” - Negation If a statement is true then its negation is false and if the statement is false then its negation is true. This can be represented in the form of a table called a “truth table.”

The Definition of Conjunction A conjunction is true only when both simple statements are true.

The Definition of Disjunction A disjunction is false only when both component statements are false.

Definitions of Negation, Conjunction, and Disjunction Negation ~: not The negation of a statement has the opposite truth value from the statement. 2. Conjunction /\: and The only case in which a conjunction is true is when both component statements are true. Disjunction: \/: or The only case in which a disjunction is false is when both component statements are false.

Constructing a Truth Table Construct a truth table for (p/\~q)\/q).

Do a truth table that includes both of the following Do a truth table that includes both of the following. ~(p/\q) and ~p\/~q Discuss the corresponding De Morgan Law. Relate it to set theory.