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

Slides:



Advertisements
Similar presentations
Sec.2-3 Deductive Reasoning
Advertisements

A Closer Look at Inductive vs. Deductive Reasoning.
A Closer Look at Inductive vs. 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.
2.4 Deductive Reasoning HW: Lesson 2.4/ 1 – 10, 13.
Deductive Reasoning. Deductive reasoning is the process of reasoning logically from given statements to a conclusion.
Chapter 2: Geometric Reasoning
Warm Up Make a conjecture based on the following information.  For points A, B and C, AB = 2, BC = 3, and AC = 4. A, B, and C form an equilateral triangle.
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 & Deductive Reasoning
Review! It’s Go Time!.
Section 2.3 Deductive Reasoning.
Using Deductive Reasoning to Verify Conjectures 2-3
2.3 Apply Deductive Reasoning. Objectives Use the Law of Detachment Use the Law of Detachment Use the Law of Syllogism Use the Law of Syllogism.
Holt McDougal Geometry 2-1 Using Inductive Reasoning to Make Conjectures 2-1 Using Inductive Reasoning to Make Conjectures Holt Geometry Warm Up Warm Up.
Today’s Lesson is on DEDUCTIVE REASONING.
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.
 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 
Thinking Mathematically Problem Solving and Critical Thinking.
2.3 – Apply Deductive Reasoning
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.
2.4 Deductive Reasoning 2.5 Postulates Geometry R/H Students will be able to distinguish between Inductive and Deductive Reasoning, and to determine the.
Ch. 2.3 Apply Deductive Reasoning
2.3 – Apply Deductive Reasoning. Deductive Reasoning: Law of Detachment: Law of Syllogism: Using facts, definitions, and logic to form a statement If.
Entry Task. Using Deductive Reasoning 2.4 Learning Target: Given a true statement I can use deductive reasoning to make valid conclusions.
2-3 Deductive Reasoning. A mechanic uses deductive reasoning to determine what is wrong with your car.
Section 2.3: Deductive Reasoning
Section 2.2 Inductive and Deductive Reasoning. Definition: Conjecture an unproven statement that is based on observations or given information.
Deductive and Inductive Reasoning
p qp q q pq p p  q ~p  ~q ~q  ~p q p September 17, 2014.
Inductive Reasoning Notes 2.1 through 2.4. Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is.
Name vertical angles and linear pairs. Name a pair of complementary angles and a pair of supplementary angles.
Do NOW: 1.) Solve 2(x – 15) = 30. Write a justification for each step. 2.) Find the next number in this sequence: 3, 5, 8, … How is the reasoning different.
2.3 Deductive Reasoning 2.4a Reasoning in Algebra.
Geometry Chapter 2: Reasoning and Introduction to Proof We can do this dude!
LG 1: Logic A Closer Look at Reasoning
Reasoning in Algebra & Deductive Reasoning (Review) Chapter 2 Section 5.
Section 2-3: Deductive Reasoning Goal: Be able to use the Law of Detachment and the Law of Syllogism. Inductive Reasoning uses _________ to make conclusions.
Using Deductive Reasoning to Verify Conjectures 2-3
2-4 Deductive Reasoning Objective:
Reasoning and Proof Unit 2.
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.
UNIT 2 Geometric Reasoning 2.1
2.4 Deductive Reasoning 2.4 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.
Applying Deductive Reasoning
Deductive Reasoning Deductive Reasoning – Reasoning that uses facts, rules, definitions, or properties to reach logical conclusions. Law of Detachment.
Inductive and Deductive Reasoning
Sec. 2.3: Apply 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.
Drawing and Supporting Conclusions
Math Humor Q: How is a geometry classroom like the United Nations?
A Closer Look at Inductive vs. Deductive Reasoning
2.3 Apply Deductive Reasoning
Drill: Wednesday, 11/1 Determine if the conditional “If x is a number then |x| > 0” is true. If false, give a counterexample. Write the contrapositive.
Notes 2.3 Deductive Reasoning.
Chapter 2.3 Notes: Apply Deductive Reasoning
A Closer Look at Inductive vs. Deductive Reasoning
UNIT 2 Geometric Reasoning 2.1
2.3 Deductive Reasoning.
A Closer Look at Inductive vs. Deductive Reasoning
2-3 Apply Deductive Reasoning
Pearson Unit 1 Topic 2: Reasoning and Proof 2-4: Deductive Reasoning Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.
Consider the following TRUE conditional statement…
Presentation transcript:

2.2 Inductive and Deductive Reasoning

Deductive reasoning is the process of reasoning logically from given statements to a conclusion.

Deductive vs. Inductive Reasoning The difference: inductive reasoning uses patterns to arrive at a conclusion (conjecture) deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion.

Examples of Inductive Reasoning 1)Every quiz has been easy. Therefore, the test will be easy. 2)The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow. 3)Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall.

Examples of Deductive Reasoning The catalog states that all entering freshmen must take a mathematics placement test. Conclusion: You will have to take a mathematics placement test. You are an entering freshman.

Inductive or Deductive Reasoning? 60 ◦ x Triangle sum property - the sum of the angles of any triangle is always 180 degrees. Therefore, angle x = 30° What is the measure of angle x? Deductive Reasoning – conclusion is based on a property

Inductive or Deductive Reasoning? Geometry example… What is the next shape in the sequence? Inductive Reasoning- conclusion based off of pattern

Deductive Reasoning Law of Detachment If a conditional is true and its hypothesis is true, then its conclusion is true. If P Q is a true statement and p is true, then q is true.

If there is lightning, then it is not safe to be out in the open. Marla sees lightning from the soccer field. It is not safe for Marla to be out in the open.

If it is snowing, then the temperature is less than or equal to 32˚F. The temperature is 20˚F. It is not possible to conclude that it is snowing.

You try! Use the law of detachment to draw a conclusion. If a baseball player is a pitcher, then that player should not pitch a complete game two days in a row. Brent is a pitcher. On Monday, he pitches a complete game. What can you conclude? Brent should not pitch a complete game on Tuesday.

You try!! Use the Law of Detachment to draw a conclusion, if possible. If two lines are parallel, then they do not intersect. Line a is parallel to line b. Line a will not intersect line b

You try! If three points lie on the same line, then they are collinear. Points A, B, and C lie on line l. Points A, B and C are collinear

You try! If a road is icy, then driving conditions are hazardous. Driving conditions are hazardous. It is not possible to conclude that it is icy.

Deductive Reasoning LAW OF SYLLOGISM If p q and q r are true statements, then p r is a true statement

Deductive Reasoning LAW OF SYLLOGISM If Tony goes to the movies, then he will eat popcorn. If Tony eats popcorn, he will get indigestion. Conclusion: If Tony goes to the movies, then he will get Indigestion. pq q r pr

Deductive Reasoning LAW OF SYLLOGISM Example: If it rains outside, the walkway will get wet. If the walkway is wet, the walkway will be slippery. What can we conclude from the Law of Syllogism? Conclusion: If it is raining, the walkway will be slippery.

You Try! Can you use Law of syllogism? If a team wins 10 games, then they play in the finals. If a team plays in the finals, then they travel to Boston. The Ravens won 10 games. Conclusion:The Ravens will travel to Boston.