Section 2.5 If-Then Statements and Deductive Reasoning pg.82.

Slides:

Advertisements

Similar presentations

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.

Advertisements

2.5 If-Then Statements and Deductive Reasoning

Geometry 2.3 Big Idea: Use Deductive Reasoning

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

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

Deductive Reasoning BY: [NAME REMOVED]. What is Deductive Reasoning  Deductive reasoning is a logical process in which a conclusion is based on the concordance.

A conditional is a statement that can be written in the If – Then form. If the team wins the semi-final, then it will play in the championship.

5-4 Inverses, Contrapositives, and Indirect Reasoning

___(0-10 pts) Describe what a conditional if-then statement and the different parts of a conditional statement. Give at least 3 examples. ___(0-10 pts)

Definitions © 2006 by Mr. Mayers Reasoning Conditional Statements Properties Undefined Terms Symmetry Team 1Team 2Team 3Team

If (-3,y) is a solution to the equation -2x+7y=-8, what is the value for y ? a / 2 b. -2 c. - 2 / 7 d warm-up 4.

2. 1 Inductive Reasoning & Conjecture 2. 2 Logic 2

Geometry Using Deductive Reasoning to Verify Conjectures

Using Deductive Reasoning to Verify Conjectures 2-3

Day 1: Logical Reasoning Unit 2. Updates & Reminders Check your grades on pinnacle Exam corrections due tomorrow Vocab Quiz Friday.

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.

Inductive vs Deductive Reasoning

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

Laws of Logic Using arguments that have logical order.

Section 2.3 Deductive Reasoning.

Warm Up Underline the hypothesis and circle the conclusion of each conditional. 1. A mapping that is a reflection is a type of transformation. 2. The quotient.

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?

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.

© 2004 Charlean Mullikin All rights reserved

2.2 Conditional Statements and 2.3 Using deductive Reasoning to Verify Conjectures.

Inductive and Deductive Reasoning. Notecard 30 Definition: Conjecture: an unproven statement that is based on observations or given information.

Section 2-2: Conditional Statements. Conditional A statement that can be written in If-then form symbol: If p —>, then q.

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.

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.

Holt McDougal Geometry 2-3 Using Deductive Reasoning to Verify Conjectures Students will… Apply the Law of Detachment and the Law of Syllogism in logical.

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

2.3 – Apply Deductive Reasoning. Deductive Reasoning: Law of Detachment: Law of Syllogism: Using facts, definitions, and logic to form a statement If.

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

FRIDAY, AUGUST 24, HOMEWORK CHECK Please pass in your write-ups then check your answers to the homework from Wednesday night: p #42-50 even.

Deductive Reasoning Geometry Chapter 2-3 Mr. Dorn.

2.3 Deductive Reasoning. Symbolic Notation Conditional Statements can be written using symbolic notation. Conditional Statements can be written using.

Lesson 2-2: Logic 1 Lesson 2-2 Logic. Lesson 2-2: Logic 2 Venn diagrams: show relationships between different sets of data. can represent conditional.

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.

Conditional Statements and Deductive Reasoning 2-1 – 2-3.

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.

Deductive Reasoning BOMLA LacyMath Geometry Pre-AP.

Essential Question: What is deductive reasoning?

Using Deductive Reasoning to Verify Conjectures 2-3

2-4 Deductive Reasoning Objective:

Biconditionals & Deductive Reasoning

Drill: Tuesday, 10/14 2. Determine if the conditional “If x is a number then |x| > 0” is true. If false, give a counterexample. OBJ: SWBAT analyze.

2.2 Continued: Deductive Reasoning

Palm trees grow in warm climates

2.4 Deductive Reasoning 2.4 Deductive Reasoning.

Apply Deductive Reasoning

Sec. 2.3: Apply Deductive Reasoning

Earlier we learned about inductive reasoning. • Earlier we learned about inductive reasoning. • Look at specific examples. • Recognize patterns, which.

Logic Lesson 2-2: Logic.

2.4 Deductive Reasoning.

Do Now Determine how a conclusion was made (by observing a pattern, facts being provided, something that is repeated, etc.) 1. Every time Katie has worn.

2-3 Deductive Reasoning Objectives:

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.

Alarms By: Mary

To solve problems by looking for a pattern

Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning

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

Conditional Statements

Presentation transcript:

Section 2.5 If-Then Statements and Deductive Reasoning pg.82

Definition If/Then Statement - a rule that says if one thing is true, then another thing is also true. If you don’t study, Then you will fail. Hypothesis - If part. The statement that must be true for the rule to apply. Conclusion - The part that can be assumed if the Hypothesis is true.

Definition If/Then Statement - a rule that says if one thing is true, then another thing is also true. If the team wins the semi-final, Then the team will play in the championship. Hypothesis - If part. The statement that must be true for the rule to apply. Conclusion - The part that can be assumed if the Hypothesis is true.

If/Then Statement Example If I pass the driving test, then I will get my driver’s license. Hypothesis - Conclusion - If I pass the driving test, then I will get my driver’s license.

If p  q and p is true then q is true. If the hypothesis is true, then the conclusion can be assumed to be true. or

Tips about Laws of Logic Law of Detachment This law involves one(1) if, then statement and another simple statement which produces another simple statement.

If the Schurz football team scores 4 touchdowns, then the football team will win. The bulldogs scores 7 touchdowns against Lane Tech. Win vs. Lane No Conclusion The bulldogs picks off 3 passes against Mather. Tavaris scores 3 touchdowns and Angel scores 2 against Von Steuben. Win vs. Dixie The team pummels Lake View. No Conclusion?

If p  q and q  r, are true, then p  r is also true. Several if/then statements can be hooked together. If the first hypothesis is true, then the last conclusion can be assumed to be true.

If Mr Patel sees your cell phone, Then he will take it from you. If Mr Patel takes your phone, Then he will call his sister in NYC. If Mr. Patel calls his sister in NYC, Then He will listen to her for over an hour. If He listens to her for over an hour, Then your roaming charges will be outrageous. Conclusion?

If Mr Patel sees your cell phone {p}, Then he will take it from you {q}. If Mr Patel takes your phone, {q} Then he will call his sister in NYC {n}. If Mr. Patel calls his sister in NYC, {n} Then He will listen to her for over an hour.{u} If He listens to her for over an hour, {u} Then your roaming charges will be outrageous. {r} Conclusion?

Tell your neighbor everything you can about this picture

More Examples Law of Detachment – If the dog barks, then it will wake the baby. Hypothesis: The dog barks. Conclusion: ?

More Examples Law of Syllogism - If the dog barks, then it will wake the baby. - If the baby wakes, then mom will be mad. Conclusion?  If mad gets mad, then you can’t go to the party.

Class Work Practice Rewrite statement as “if, then” statement 1.Every game on my computer is fun to play.  If a game is on my computer, then it is fun to play

Class Work Practice Rewrite statement as “if, then” statement 2. I will buy the CD if it costs less than $15  If the CD costs less that $15, then I will buy it.

Class Work Practice Rewrite statement as “if, then” statement 3. All teachers at Schurz High School have taught for at least 5 years.  If a teacher works at Schurz, then he or she has taught for at least 5 years.

Class Work Practice Rewrite statement as “if, then” statement 4. An angle is obtuse if its measure is 170 degrees  If the measure of an angle is 170, then the angle is obtuse.

Class Work Practice What can you conclude from the given true statements 6. If you study at least two hours for the test, then you will pass the test. You study three hours for the test.  You will pass the test.

Class Work Practice What can you conclude from the given true statements 6. If x has a value of 7, then 2x – 3 has a value of 11. The value of x is 7.  2x-3 has a value of 11.

Homework pg.85 #7-15