Laws of Logic Using arguments that have logical order.

Slides:



Advertisements
Similar presentations
1/15/ : Truth and Validity in Logical Arguments Expectations: L3.2.1: Know and use the terms of basic logic L3.3.3: Explain the difference between.
Advertisements

EXAMPLE 1 Use the Law of Detachment
Honors Geometry Section 4.6 (1) Conditions for Special Quadrilaterals
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.
CAHSEE W. UP GEOMTRY GAME PLAN Date9/24/13 Tuesday Section / TopicNotes #19: 2.2 Definitions & Biconditional Statements Lesson GoalSTUDENTS WILL BE ABLE.
Bell Work 1) Find the value of the variables 2)Write the conditional and converse of each biconditional, and state if the biconditional is true or false.
4.3 Warm Up Find the distance between the points. Then find the midpoint between the points. (5, 2), (3, 8) (7, -1), (-5, 3) (-9, -5), (7, -14)
Problems to study for the chapter 2 exam
Check your skills 2. Homework Check Notes 4. Practice 5. Homework/work on Projects.
Inductive and Deductive Reasoning Geometry 1.0 – Students demonstrate understanding by identifying and giving examples of inductive and deductive reasoning.
Day 1: Logical Reasoning Unit 2. Updates & Reminders Check your grades on pinnacle Exam corrections due tomorrow Vocab Quiz Friday.
Laws of Logic Law of Detachment If p  q is a true conditional statement AND p is true, then you can conclude q is true Example If you are a sophomore.
Inductive vs Deductive Reasoning
Bell Ringer.
2.3: Deductive Reasoning p Deductive Reasoning Use facts, definitions and accepted properties in logical order to write a logical argument.
Review! It’s Go Time!.
Section 2.3 Deductive Reasoning.
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.
Chapter 2.3 Notes: Apply Deductive Reasoning Goal: You will use deductive reasoning to form 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.
Lesson 2-4 Deductive Reasoning Deductive reasoning- uses facts, rules, definitions, or properties to reach logical conclusions Law of Detachment: If p.
2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning.
EXAMPLE 1 Use the Law of Detachment Use the Law of Detachment to make a valid conclusion in the true situation. If two segments have the same length, then.
#tbt #4 Who Owns The Zebra?
1. Grab board/marker for your group 2. Do WarmUp below V S T M P R TP bisects VS and MR. VM is congruent to SR. MP = 9, VT = 6 Perimeter of MRSV = 62 Find.
Section 2-5: Deductive Reasoning Goal: Be able to use the Law of Detachment and the Law of Syllogism. Inductive Reasoning uses _________ to make conclusions.
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.
Deductive Reasoning (G.1d) Obj: SWBAT apply the laws of validity: Detachment, Contrapositive & Syllogism and the symbolic form (2.4). Homework (day 20)
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.
Honors Geometry Chapter 2 Review!. Name the property illustrated below. If segment AB is congruent to segment CD, then AB=CD. A.) definition of a midpoint.
“Education is the most powerful weapon which you can use to change the world.” ― Nelson Mandela Do NowNelson Mandela  Put your homework assignment (examples.
2.3 – Apply Deductive Reasoning. Deductive Reasoning: Law of Detachment: Law of Syllogism: Using facts, definitions, and logic to form a statement If.
Deductive Reasoning Geometry Chapter 2-3 Mr. Dorn.
2.3 Deductive Reasoning p. 87 Reminders Statement Conditional statement Converse Inverse Contrapositive Biconditional Symbols p → q q → p ~p → ~q ~q.
Properties, Postulates, & Theorems Conditionals, Biconditionals,
2.3 Deductive Reasoning. Symbolic Notation Conditional Statements can be written using symbolic notation. Conditional Statements can be written using.
2-1 Inductive Reasoning and Conjecturing. I. Study of Geometry Inductive reasoning Conjecture Counterexample.
Reasoning and Proof Chapter – Conditional Statements Conditional statements – If, then form If – hypothesis Then – conclusion Negation of a statement-
3/15/ : Deductive Reasoning1 Expectations: L3.1.1: Distinguish between inductive and deductive reasoning, identifying and providing examples of each.
EXAMPLE 1 Draw Conclusions In the diagram, AB BC. What can you conclude about 1 and 2 ? SOLUTION AB and BC are perpendicular, so by Theorem 3.9, they form.
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.
Spring Student Performance Analysis Presentation may be paused and resumed using the arrow keys or the mouse. Geometry Standards of Learning.
2.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply Deductive Reasoning.
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.
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.
Topic 1: 1.5 – 1.8 Goals and Common Core Standards Ms. Helgeson
Essential Question: What is deductive reasoning?
Goal: To learn about and use deductive reasoning.
2-3 Apply Deductive Reasoning
2.2 Continued: Deductive Reasoning
Geometry Ch. 2 Review Created by Educational Technology Network
2-4 Deductive Reasoning Ms. Andrejko.
Sec. 2.3: Apply Deductive Reasoning
Geometry Review PPT Finnegan 2013
Perpendicular Definition: Lines that meet at a 90 degree angle.
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
1-5 Angle Relations.
Lesson 2 – 4 Deductive Reasoning
Chapter 2.3 Notes: Apply Deductive Reasoning
Reasoning and Proofs Deductive Reasoning Conditional Statement
2-3 Apply Deductive Reasoning
Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning
Chapter 2.3 Notes: Apply Deductive Reasoning
Presentation transcript:

Laws of Logic Using arguments that have logical order

Review Terms Counterexample Conditional Statement Hypothesis Conclusion

If Osama Bin Laden dies, the US troops will come home. The troops came back home. Conclusion: Osama is dead. 1.Identify the conditional statement. 2.Identify the hypothesis and conclusion. 3.Is this true? 4.Justify your answer.

If you eat too much ice cream, you will get sick. You’re sick. Conclusion: You had too much ice cream. 1.Identify the conditional statement. 2.Identify the hypothesis and conclusion. 3.Is this true? 4.Justify your answer.

Law of Detachment If p  q is a true conditional statement and p (hypothesis) is true, then q (conclusion) is true. p  q true p true  q true

Law of Detachment If you save a penny then you earn a penny. Julio saves a penny. Therefore, Julio earns a penny Why is this argument valid?Because it follows the law of detachment. p  q true p true  q true p: save a penny q: earn a penny TRUE conditional statement TRUE hypothesis You can conclude that the conclusion is TRUE Given Conclusion

Law of Detachment If you pay attention then you will learn. Mara pays attention. Therefore, Mara will learn. Why is this argument valid?Because it follows the law of detachment. p  q true p true  q true p: pay attention q: will learn TRUE conditional statement TRUE hypothesis You can conclude that the conclusion is TRUE Given Conclusion

Law of Detachment If you exercise then you will be healthy. Tony is healthy. Therefore, Tony exercises. Why is this argument invalid?Because it does not follow the law of detachment. p  q true p true  q true p: exercise q: healthy TRUE This is not the hypothesis You cannot conclude that this statement is TRUE Given Conclusion

Which argument is valid? Vertical angles are congruent  A   B Therefore  A and  B are vertical angles Vertical angles are congruent  A and  B are vertical angles Therefore  A   B Invalid Valid

Which argument is valid? If two lines are perpendicular, then they intersect to form right angles. Lines l and m intersect to form right angles Therefore, line l is perpendicular to line m If two lines are perpendicular, then they intersect to form right angles. Line l is perpendicular to line m Therefore, lines l and m intersect to form right angles Invalid Valid

Which argument is valid? The menu says that apple pie a la mode is served with ice cream. Laura ordered apple pie a la mode. Therefore, she was served ice cream. The menu says that apple pie a la mode is served with ice cream. Laura ordered ice cream. Therefore, she was served apple pie a la mode. Valid Invalid

What can you conclude? Linear pairs are adjacent angles that measure 180°.  A and  B are linear pairs Therefore,  A and  B are adjacent angles and they measure 180°. Linear pairs are adjacent angles that measure 180°.  A and  B are adjacent angles Therefore, This argument does not follow the Law of Detachment so I can not make a conclusion

Law of Detachment Sarah knows that all sophomores take driver education at her school. Hank is taking driver education. So Hank is a sophomore. If m  ABC<90 , then  ABC is an acute angle. m  ABC = 42  degrees. So  ABC is an acute angle 1. Explain why this argument is valid/not valid. 2. Justify your answer. 3. What do you need to change to make a valid argument not valid and the not valid one valid.

Closure Michael knows that if he does not do his chores in the morning, he will not be allowed to play video games later the same day. Michael does not play video games on Friday afternoon. So Michael did not do his chores on Friday morning. If two angles are vertical, then they are congruent.  ABC and  DBE are vertical. So  ABC and  DBE are congruent. Which statement is valid and which is not valid. Justify your answer.

Law of Syllogism If p  q and q  r are true conditional then p  r is true. How is the conclusion of the first conditional statement related to the hypothesis of the second conditional statement. p  q true q  r true  p  r true

You can conclude this statement is TRUE Conclusion Law of Syllogism If the sun is shining then it is a beautiful day. If it is a beautiful day, then we will have a picnic. Therefore if the sun is shining then we will have a picnic. TRUE conditional statements Given p  q true q  r true  p  r true p: sun is shining q: beautiful day r: have a picnic Why is this argument valid?Because it follows the law of syllogism.

You can conclude this statement is TRUE Conclusion Law of Syllogism If you take algebra 1 then you will take geometry. If you take geometry, then you will take algebra 2. Therefore if you take algebra 1 then you will take algebra 2. TRUE conditional statements Given p  q true q  r true  p  r true p: algebra 1 q: geometry r: algebra 2 Why is this argument valid?Because it follows the law of syllogism.

You can conclude this statement is TRUE Conclusion Law of Syllogism If you get the new job then you will be able to take the Mertolink. If you take the Metrolink, then you will not have to buy a new car. If you don’t have to buy an new car then you will not need to get insurance. If you get the new job then you will not need to get insurance. TRUE conditional statements Given p  q true q  r true r  s  true p  s  true p: get the new job q: take the Metrolink r: do not have to buy a new car s: do not need insurance Why is this argument valid?Because it follows the law of syllogism. Given

Not the correct conclusion Conclusion Law of Syllogism If  2 is acute then  3 is obtuse. If  3 is obtuse, then  4 is acute. Therefore if you  4 is acute then  2 is acute TRUE conditional statements Given p  q true q  r true  p  r true p:  2 is acute q:  B is obtuse r:  4 is acute Why is this argument invalid? Because it doesn’t follow the law of syllogism.

Which argument is valid? Valid Invalid If the two lines are parallel then the lines do not intersect. If the lines don’t intersect, then no angles are formed. Therefore if the two lines are parallel then the no angles are formed. If the two lines are parallel then the lines do not intersect. If the lines don’t intersect, then we will no angles are formed. Therefore if no angles are formed then the two lines are parallel

Which argument is valid? Valid Invalid If we visit Hong Kong, then we will eat well. If we eat well, then we will walk a lot. If we visit Hong Kong then we will walk a lot. If we visit Hong Kong, then we will eat well. If we visit Hong Kong, we will walk a lot. If we eat well then we will walk a lot.

Which argument is valid? Invalid Valid If we visit Disneyland then we will see Mickey Mouse. If we visit Disneyland then we will get on Space Mountain. If we get on Space Mountain then we will have fun. If we see Mickey Mouse then we get on Space Mountain. If we visit Disneyland then we will see Mickey Mouse. If we visit Disneyland then we will get on Space Mountain. If we get on Space Mountain then we will have fun. If we visit Disneyland then we will have fun.

If Don is going, then Eve is going. Ben is not going to the party. If Al is going then, Ben is going. If Carla is going, then Don is going Al or Carla is going to the party. Is Ben going to the party? Is Al going to the party? Is Carla going to the party? Is Don going to the party? Is Eve going to the party? Who is going to the Party? Using the Law of Detachment and the Law of Syllogism     