2.3: Deductive Reasoning p. 85-91. Deductive Reasoning Use facts, definitions and accepted properties in logical order to write a logical argument.

Slides:



Advertisements
Similar presentations
Sec.2-3 Deductive Reasoning
Advertisements

Sec 2-3 Concept: Deductive Reasoning Objective: Given a statement, use the laws of logic to form conclusions and determine if the statement is true through.
2.5 If-Then Statements and Deductive Reasoning
Geometry 2.3 Big Idea: Use Deductive Reasoning
Answers to the HW p. 75 #10-20 even, all, 55 & 56
2. 1 Inductive Reasoning & Conjecture 2. 2 Logic 2
GEOMETRY Chapter 2 Notes.
Inductive and Deductive Reasoning Geometry 1.0 – Students demonstrate understanding by identifying and giving examples of inductive and deductive reasoning.
Inductive vs Deductive Reasoning
Bell Ringer.
Laws of Logic. Deductive Reasoning Uses the following to form logical arguments. Facts Example: All humans breath air. Definitions Example: Two lines.
Warm Up 1. How do I know the following must be false? Points P, Q, and R are coplanar. They lie on plane m. They also lie on another plane, plane n. 2.
Laws of Logic Using arguments that have logical order.
Section 2.3 Deductive Reasoning.
Introduction to Geometric Proof Logical Reasoning and Conditional Statements.
Chapter 2.3 Notes: Apply Deductive Reasoning Goal: You will use deductive reasoning to form a logical argument.
Section 2-3 Deductive Reasoning. Types of Reasoning:
Write the following in biconditional form. p: The sun is out. q: It is day time. The sun is out iff it is day time.
Deductive Reasoning What can you D…D….D…. DEDUCE ?
2.4 Deductive Reasoning Deductive Reasoning – Sometimes called logical reasoning. – The process of reasoning logically from given statements or facts to.
Deductive Reasoning Chapter 2 Lesson 4.
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.
2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning.
Deductive Structure Statements of Logic. The Structure.
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.
Do Now. Law of Syllogism ◦ We can draw a conclusion when we are given two true conditional statements. ◦ The conclusion of one statement is the hypothesis.
Ch. 2.3 Apply Deductive Reasoning
Deductive Reasoning Geometry Chapter 2-3 Mr. Dorn.
Section 2.3: Deductive Reasoning
2.3 Deductive Reasoning. Symbolic Notation Conditional Statements can be written using symbolic notation. Conditional Statements can be written using.
Inductive Reasoning Notes 2.1 through 2.4. Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is.
Chapter 2 Section 2.3 Apply Deductive Reasoning. Deductive Reasoning Uses facts, definitions, accepted properties, and the laws of logic to form a logical.
Name vertical angles and linear pairs. Name a pair of complementary angles and a pair of supplementary angles.
Geometry 2-6 Review Problems Unit 2 – Reasoning and Proof.
Chapter 2, Section 1 Conditional Statements. Conditional Statement Also know as an “If-then” statement. If it’s Monday, then I will go to school. Hypothesis:
Reasoning in Algebra & Deductive Reasoning (Review) Chapter 2 Section 5.
Essential Question: What is deductive reasoning?
2-4 Deductive Reasoning Objective:
Section 2.3 – Deductive Reasoning
Deductive Reasoning, Postulates, and Proofs
2-3 Apply Deductive Reasoning
Biconditionals & Deductive Reasoning
2.2 Inductive and Deductive Reasoning
Do Now: True 2. False 3. False C D.
Apply Deductive Reasoning
2-4 Deductive Reasoning Ms. Andrejko.
} { Using facts, definitions, accepted properties and the
Applying Deductive Reasoning
2.2 Deductive Reasoning Objective:
Clickers Bellwork Translate the following statement into a conditional statement Angles measuring less than 90o are acute angles Write the converse, inverse.
Sec. 2.3: Apply Deductive Reasoning
2.4 Deductive Reasoning.
Warmup Definition: Perpendicular Lines—
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.
2-3 Deductive Reasoning Objectives:
Venn Diagrams & Deductive Reasoning
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.
1. Write the converse, inverse, and contrapositive of the conditional below and determine the truth value for each. “If the measure of an angle is less.
2.3 Apply Deductive Reasoning
2-4 Deductive Reasoning 8th Grade Geometry.
Notes 2.3 Deductive Reasoning.
Chapter 2.3 Notes: Apply Deductive Reasoning
Section 3-6 Inductive Reasoning.
2-3 Apply Deductive Reasoning
2-4 Deductive Reasoning Deductive Reasoning: Using facts, rules, definitions, or properties to reach logical conclusions. Law of Detachment: A form.
Law of Detachment Law of Syllogism
2-4 Deductive Reasoning Vocab:
Chapter 2.3 Notes: Apply Deductive Reasoning
4.4: Analyze Conditional Statements.
Presentation transcript:

2.3: Deductive Reasoning p

Deductive Reasoning Use facts, definitions and accepted properties in logical order to write a logical argument.

Law of Detachment If p q is a true conditional statement and p is true, then q is true. Ex. 1)If I pass the test, then I get an A in geometry. (p q) 2)I passed the test.(p) 3)So I got an A in geometry.(q)

Law of Syllogism If p q and q r are true conditional statements, then p r is true. Ex. 1) If I pass the test, then I get an A in geometry. 2) If I get an A in geometry, then I get a new car. 3) I passed the test so I get a new car.

Ex 1. Law of Detachment or Law of Syllogism or neither 1. If an angle is acute, then it is not obtuse. 2. <ABC is acute. 3. <ABC is not obtuse. Valid by Law of Detachment

Ex 2. Law of Detachment or Law of Syllogism or neither 1. Right angles are congruent. 2. <A <B 3. <A and <B are right angles. Invalid. Statement 2 is not related to the hypothesis

Ex 3.Law of Detachment or Law of Syllogism 1. If you save a penny, then you have earned a penny. 2. Art saves a penny. 3. Art has earned a penny. Valid by Law of Detachment.

Ex 4. Law of Detachment or Law of Syllogism or neither 1. If you are a teenager, then you are always right. 2. If you are always right, then people will listen to you. 3. If you are a teenager, then people will listen to you. Valid by Law of Syllogism.

Ex 5. Law of Detachment or Law of Syllogism 1. If you drive 50 miles per hour in a school zone, then you will get a speeding ticket. 2. Pat received a speeding ticket. 3. Pat was driving 50 miles per hour in a school zone. Invalid. Pat could have received a speeding ticket for speeding on the highway.

For the following examples, write a conclusion using the true statements. If no conclusion is possible, write no conclusion. State the applicable law.

Example 1 If Jim gets stung by a bee, then he will get very ill. If he gets very ill, then he will go to the hospital. Jim gets stung by a bee. Conclusion? Jim will go to the hospital. Law of Syllogism

Example 2 If two planes intersect, then their intersection is a line. Plane T and plane W intersect. Conclusion? Plane T and plane W intersect in a line. Law of Detachment

Example 3 If you cut class, then you will receive ISS. You cut class. Conclusion? You received ISS. Law of Detachment

Example 4 If Mike doesn’t work hard, then he won’t start the game and will quit the team. Mike quit the team. Conclusion? No conclusion. We do not why he quit the team.