2.3 Deductive Reasoning 2.4a Reasoning in Algebra.

Slides:

Advertisements

Similar presentations

Geometry Chapter 2 Terms.

Advertisements

Sec.2-3 Deductive Reasoning

Deductive Reasoning. Objectives I can identify an example of inductive reasoning. I can give an example of inductive reasoning. I can identify an example.

2.5 - I F -T HEN S TATEMENTS AND D EDUCTIVE R EASONING Homework #6.

Chapter 2 Geometric Reasoning

Lesson 2.3 p. 87 Deductive Reasoning Goals: to use symbolic notation to apply the laws of logic.

2-4 Rules of Logic What is deductive reasoning?

Geometry Using Deductive Reasoning to Verify Conjectures

Inductive and Deductive Reasoning Geometry 1.0 – Students demonstrate understanding by identifying and giving examples of inductive and deductive reasoning.

Chapter 2: Geometric Reasoning

Deductive Reasoning 2-3. Deductive Reasoning Example 1  Suppose that a mechanic knows that if a car has a dead battery, the car will not start. A mechanic.

Inductive vs Deductive Reasoning

Section 1.1 Inductive Reasoning 1/16. DEDUCTIVE REASONING Two Types of Reasoning INDUCTIVE REASONING 2/16.

Using Deductive Reasoning to Verify Conjectures 2-3

1 2-3 Deductive Reasoning Objectives: Define deductive reasoning Use the Law of Detachment Use the Law of Syllogism.

Chapter 2.3 Notes: Apply Deductive Reasoning Goal: You will use deductive reasoning to form a logical argument.

Holt McDougal Geometry 2-3 Using Deductive Reasoning to Verify Conjectures Determine if each conjecture is true or false. If false, provide a counterexample.

Today’s Lesson is on DEDUCTIVE REASONING.

Section 2-3 Deductive Reasoning. Types of Reasoning:

Deductive Reasoning What can you D…D….D…. DEDUCE ?

Bell Work “If x=4, then “ 1)Write the hypothesis 2)Write the Conclusion 3) Write the converse 4)What is the Biconditional?

Applying Deductive Reasoning Section 2.3. Essential Question How do you construct a logical argument?

Deductive Reasoning Chapter 2 Lesson 4.

Chapter 2 Lesson 3 Objective: To use the Law of Detachment and the Law of Syllogism.

Deductive Reasoning.  Conditional Statements can be written using symbolic notation  p represents hypothesis  q represents conclusion  is read as.

 ESSENTIAL QUESTION  How can you use reasoning to solve problems?  Scholars will  Use the Law of Syllogism  Use the Law of Detachment UNIT 01 – LESSON.

2.4 Ms. Verdino.  Biconditional Statement: use this symbol ↔  Example ◦ Biconditional Statement: The weather is good if and only if the sun is out 

2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning.

Read with purpose and meaning.. Drawing conclusions refers to information that is implied or inferred. This means that the information is never clearly.

Section 3.3 Using Laws of Logic. Using contrapositives  The negation of a hypothesis or of a conclusion is formed by denying the original hypothesis.

WARM UP. DEDUCTIVE REASONING LEARNING OUTCOMES I will be able to use the law of detachment and syllogism to make conjectures from other statements I.

C HAPTER Using deductive reasoning. O BJECTIVES Students will be able to: Apply the Law of Detachment and the Law of Syllogism in logical reasoning.

Welcome to Social Studies Happy Monday! Mrs. Gallagher Team Hilton.

2.2 Inductive and Deductive Reasoning. Deductive reasoning is the process of reasoning logically from given statements to a conclusion.

Ch. 2.3 Apply Deductive Reasoning

Lesson 21 LAW OF DETACHMENT AND SYLLOGISM. Review and New Vocabulary Inductive reasoning is the process of reasoning that a rule or statement is true.

Section 2-4: Deductive Reasoning Objectives: Use the Law of Detachment Use the Law of Syllogism Inductive Reasoning: based on observing what has happened.

Entry Task. Using Deductive Reasoning 2.4 Learning Target: Given a true statement I can use deductive reasoning to make valid conclusions.

CONFIDENTIAL 1 Grade 9 Algebra1 Using Deductive Reasoning to Verify Conjectures.

Section 2.3: Deductive Reasoning

3/15/ : Deductive Reasoning1 Expectations: L3.1.1: Distinguish between inductive and deductive reasoning, identifying and providing examples of each.

2.3 DEDUCTIVE REASONING GOAL 1 Use symbolic notation to represent logical statements GOAL 2 Form conclusions by applying the laws of logic to true statements.

Deductive Reasoning. Warm-up Objectives: 1) To use the Law of Detachment 2) To use the Law of Syllogism.

LG 1: Logic A Closer Look at Reasoning

2-4 Deductive Reasoning. Deductive Reasoning …(sometimes called Logical Reasoning) is the process of reasoning logically from given statements or facts.

Reasoning in Algebra & Deductive Reasoning (Review) Chapter 2 Section 5.

Section 2.3 – Deductive Reasoning

2-3 Apply Deductive Reasoning

Biconditionals & Deductive Reasoning

Warm Up For this conditional statement: If a polygon has 3 sides, then it is a triangle. Write the converse, the inverse, the contrapositive, and the.

2.2 Inductive and Deductive Reasoning

Entry Task Complete the Solve It activity on the top of page 106.

Objective Apply the Law of Detachment and the Law of Syllogism in logical reasoning.

CST 24 – Logic.

Do Now: Name each point , line, and line segment, or ray

Using Deductive Reasoning to Verify Conjectures 2-3

Sec. 2.3: Apply Deductive Reasoning

2.4 Deductive Reasoning.

Warmup Write the two conditionals(conditional and converse) that make up this biconditional: An angle is acute if and only if its measure is between 0.

Drill: Tuesday, 10/18 2. Determine if the conditional “If x is a number then |x| > 0” is true. If false, give a counterexample. OBJ: SWBAT analyze.

2.3 Apply Deductive Reasoning

Notes 2.3 Deductive Reasoning.

Chapter 2.3 Notes: Apply Deductive Reasoning

Section 3-6 Inductive Reasoning.

2.3 Deductive Reasoning.

2-3 Apply Deductive Reasoning

2.3 Deductive reasoning Brett Solberg AHS ’11-’12.

2-4 Deductive Reasoning Vocab:

Goal 1: Using Symbolic Notation Goal 2: Using the Laws of Logic

Chapter 2.3 Notes: Apply Deductive Reasoning

Presentation transcript:

2.3 Deductive Reasoning 2.4a Reasoning in Algebra

Today we will… Learning Target: Making inferences using the Law of Detachment and the Law of Syllogism.

Purpose (Please read/don’t write): You hear screeching tires, then a loud crash and breaking glass. You see nothing, but you infer that there has been a car accident. We all know the sounds of screeching tires and a crash. We know that these sounds almost always mean a car accident. But there could be some other reason, and therefore another explanation, for the sounds. Perhaps it was not an accident involving two moving vehicles. Maybe an angry driver rammed a parked car. Or maybe someone played the sound of a car crash from an iPod or a recording. Making inferences means choosing the most likely explanation from the facts at hand.

Types of Reasoning With your group, find the next two terms of the patterns: 1, 3, 7, 13, 21, … 2.1, -2.11, 2.111, , … Inductive reasoning – observing what has happened and making a conjecture about what will happen. Deductive Reasoning (logical reasoning): the process of reasoning logically from given statements (ex: definition and theorems) to a conclusion. If the given statements are true in the situation, then the conclusion is also true. Ex: a physician sees a patient with certain symptoms and uses that information to diagnose the illness

Law of Detachment Ex 1: If a car’s battery is dead, then it will not start. A mechanic works on a car and finds that its battery is dead. What can we conclude? Ex 2: If a baseball player is a pitcher, then he should not play complete games on consecutive days. A baseball player pitches a complete game on Monday. What can we conclude about Tuesday’s game? Law of Detachment: If a conditional is true and its hypothesis is true, then its conclusion is true. Symbolic: If p q is a true statement and p is true, then q is true. Be careful: If it is snowing, then is the temperature is 32 o or lower. It is 20 o. Can I conclude that it is snowing?

Law of Syllogism Law of Syllogism: If p q and q r are true statements, then p r is a true statement. Ex 1: If Megan eats candy, then she will choose purple candy. If candy is purple, then it is grape flavored candy. Conclude: If Megan eats candy, then. Ex 2: If a figure is a square, then it is a rectangle. If a figure is a rectangle, then it is a parallelogram. Conclude: If a figure is a square, then. Be careful: If a number ends in 6, then it is divisible by 2. If a number ends in 4, then it is divisible by 2. Conclude: impossible – the conclusion of one statement is not the hypothesis of the other statement

All Together Ex: Use the Law of Detachment and the Law of Syllogism to draw conclusions… a. If you live in Fort Collins, then you live in Larimer County. If you live in Larimer County, then you live in Northern Colorado. b. If you live in Fort Collins, then you live in Larimer County. Annie lives in Fort Collins. From LOS: From LOD:

Properties (on theorem sheet)

Properties (on theorem sheet)

2.3 Deductive Reasoning 2.4a Reasoning in Algebra HW: p. 96 #2-20 even, 32, 40