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

Slides:

Advertisements

Similar presentations

TRUTH TABLES Section 1.3.

Advertisements

Lesson 2-2 Logic. Ohio Content Standards: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example,

Introduction to Symbolic Logic

Logic, Conditional statements and deductive reasoning

2-2 Logic You found counterexamples for false conjectures. Determine truth values of negations, conjunctions, and disjunctions, and represent them using.

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

 Identify postulates using diagrams.  Identify and use basic postulates about points, lines, and planes.  A postulate or an axiom is a statement that.

L OGIC. A conjecture is an educated guess that can be either true or false. A statement is a sentence that is either true or false but not both. Often.

Ch.2 Reasoning and Proof Pages Inductive Reasoning and Conjecture (p.62) - A conjecture is an educated guess based on known information.

L OGIC Sol: G.1 b, c Sec: A conjecture is an educated guess that can be either true or false. A statement is a sentence that is either true or.

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

C I AC I AD U OD U O disjunction conjunction union intersection orand U U Notes 4.2 Compound Inequalities unite, combinewhere they cross, what they share.

Barnett/Ziegler/Byleen Finite Mathematics 11e1 Chapter 7 Review Important Terms, Symbols, Concepts 7.1. Logic A proposition is a statement (not a question.

LOGIC Chapter 2 – Lesson 2. LOGIC  Objectives Determine truth values of negations, conjunctions, and disjunctions, and represent them using Venn diagrams.

Vocabulary Statement--A sentence that is either true or false, but not both. Truth value--The true or false nature of a statement Compound statement--Two.

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

Over Lesson 2–1 5-Minute Check 1 A.30 B.34 C.36 D.40 Make a conjecture about the next item in the sequence. 1, 4, 9, 16, 25.

Thinking Mathematically

Welcome to Interactive Chalkboard

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–1) Then/Now New Vocabulary Example 1:Truth Values of Conjunctions Example 2:Truth Values of.

Logic Statement-any sentence that is either true or false Statement-any sentence that is either true or false Truth value-the truth or falsity of a statement.

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.

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,

Lesson 2-2 Conditional Statements 1 Lesson 2-2 Counterexamples.

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

Logic LESSON 2–2. Lesson Menu Five-Minute Check (over Lesson 2–1) TEKS Then/Now New Vocabulary Example 1:Truth Values of Conjunctions Example 2:Truth.

 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.

MID CHAPTER 2 QUIZ REVIEW SECTIONS 2.1, 1.4-5, 2.5.

MAKE SURE YOUR ASSIGNMENTS AND ASSIGNMENTS PAGE IS ON YOUR DESK. Quietly begin working on the warm- up.

Truth Tables for Negation, Conjunction, and Disjunction

Presented by: Tutorial Services The Math Center

Lesson 2-2.A Logic: Venn Diagrams.

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

Geometry Pre-AP BOMLA LacyMath 10/6.

Patterns and Conjecture

Warm Up Challenge 1. The complement of an angle is 10 less than half the measure of the supplement of the angle. What is the measure of the supplement.

Chapter 8 Logic Topics

Identify and use basic postulates about points, lines, and planes.

Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.

Discrete Mathematics Lecture 2: Propositional Logic

Statements joined by “And” (Conjunctions)

Inductive Reasoning and Conjecture, and Logic

Statements of Symbolic Logic

And represent them using Venn Diagrams.

Section 3.2 Truth Tables for Negation, Conjunction, and Disjunction

Looking at several specific situations to arrive at an educated guess is called __________. guessing B. a conjecture C. inductive reasoning D. deductive.

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

CHAPTER 3 Logic.

Welcome to Interactive Chalkboard

Presentation transcript:

Splash Screen

Then/Now You found counterexamples for false conjectures. (Lesson 2–1) Determine truth values of negations, conjunctions, and disjunctions, and represent them using Venn diagrams. Find counterexamples.

Vocabulary statement truth value negation compound statement conjunction disjunction truth table

Example 1 Truth Values of Conjunctions A. Use the following statements to write a compound statement for the conjunction p and q. Then find its truth value. p: One foot is 14 inches. q: September has 30 days. r: A plane is defined by three noncollinear points. Answer:p and q: One foot is 14 inches, and September has 30 days. Although q is true, p is false. So, the conjunction of p and q is false.

Example 1 Truth Values of Conjunctions B. Use the following statements to write a compound statement for the conjunction ~p  r. Then find its truth value. p: One foot is 14 inches. q: September has 30 days. r: A plane is defined by three noncollinear points. Answer:~p  r: A foot is not 14 inches, and a plane is defined by three noncollinear points. ~p  r is true, because ~p is true and r is true.

Example 2 Truth Values of Disjunctions A. Use the following statements to write a compound statement for the disjunction p or q. Then find its truth value. p: is proper notation for “segment AB.” q:Centimeters are metric units. r:9 is a prime number. Answer: is proper notation for “segment AB,” or centimeters are metric units. Both p and q are true, so p or q is true.

Example 2 Truth Values of Disjunctions Answer: Centimeters are metric units, or 9 is a prime number. q  r is true because q is true. It does not matter that r is false. B. Use the following statements to write a compound statement for the disjunction q  r. Then find its truth value. p: is proper notation for “segment AB.” q:Centimeters are metric units. r:9 is a prime number.

Example 2 Truth Values of Disjunctions C. Use the following statements to write a compound statement for the disjunction ~p  r. Then find its truth value. p: is proper notation for “segment AB.” q:Centimeters are metric units. r:9 is a prime number. Answer: AB is not proper notation for “segment AB,” or 9 is a prime number. Since not p and r are both false, ~p  r is false. ___

Concept

Example 3 Construct Truth Tables A. Construct a truth table for ~p  q. Step 1Make columns with the heading p, q, ~p, and ~p  q.

Example 3 Construct Truth Tables A. Construct a truth table for ~p  q. Step 2List the possible combinations of truth values for p and q.

Example 3 Construct Truth Tables A. Construct a truth table for ~p  q. Step 3Use the truth values of p to determine the truth values of ~p.

Example 3 Construct Truth Tables A. Construct a truth table for ~p  q. Step 4Use the truth values of ~p and q to write the truth values for ~p  q. Answer:

Example 3 Construct Truth Tables B. Construct a truth table for p  (~q  r). Step 1Make columns with the headings p, q, r, ~q, ~q  r, and p  (~q  r).

Example 3 Construct Truth Tables B. Construct a truth table for p  (~q  r). Step 2List the possible combinations of truth values for p, q, and r.

Example 3 Construct Truth Tables B. Construct a truth table for p  (~q  r). Step 3Use the truth values of q to determine the truth values of ~q.

Example 3 Construct Truth Tables B. Construct a truth table for p  (~q  r). Step 4Use the truth values for ~q and r to write the truth values for ~q  r.

Example 3 Construct Truth Tables B. Construct a truth table for p  (~q  r). Step 5Use the truth values for ~q  r and p to write the truth values for p  (~q  r). Answer:

Example 4 Use Venn Diagrams DANCING The Venn diagram shows the number of students enrolled in Monique’s Dance School for tap, jazz, and ballet classes. A. How many students are enrolled in all three classes? The students that are enrolled in all three classes are represented by the intersection of all three sets. Answer: There are 9 students enrolled in all three classes.

Example 4 Use Venn Diagrams DANCING The Venn diagram shows the number of students enrolled in Monique’s Dance School for tap, jazz, and ballet classes. B. How many students are enrolled in tap or ballet? The students that are enrolled in tap or ballet are represented by the union of these two sets. Answer:There are or 121 students enrolled in tap or ballet.

Example 4 Use Venn Diagrams DANCING The Venn diagram shows the number of students enrolled in Monique’s Dance School for tap, jazz, and ballet classes. C. How many students are enrolled in jazz and ballet, but not tap? The students that are enrolled in jazz and ballet, but not tap, are represented by the intersection of jazz and ballet minus any students enrolled in tap. Answer:There are – 9 or 25 students enrolled in jazz and ballet, but not tap.

End of the Lesson