Lesson 2 – 4 Deductive Reasoning Geometry Lesson 2 – 4 Deductive Reasoning Objective: Use the Law of Detachment. Use the Law of Syllogism.

Deductive Reasoning What is inductive reasoning? Deductive reasoning Drawing conclusions based upon patterns Deductive reasoning Drawing conclusions based upon facts, rules, definitions or properties.

Determine whether each conclusion is based on inductive or deductive reasoning. Every time Katie has worn her favorite socks to a softball game, she has gotten at least one hit. Katie is wearing her favorite socks to a game tonight, so she concludes that she will get at least one hit. If John is late making his car insurance payment, he will be assessed a late fee of $50. John’s payment is late this month, so he concludes that he will be assessed a late fee of $50. Inductive Deductive

Determine whether each conclusion is based on inductive or deductive reasoning. Sandra learned that if it is cloudy at night it will not be as cold in the morning than if there are no clouds at night. Sandra knows it will be cloudy tonight, so she believes it will be not be cold tomorrow. Deductive Since this is a science fact

Determine whether each conclusion is based on inductive or deductive reasoning. In Miguel’s town, the month of April has had the most rain for the past 5 years. He thinks that April will have the most rain this year. All of the signature items on a restaurant's menu shown are noted with a special symbol. Kevin orders a menu item that has this symbol next to it, so he concludes that the menu item that he has ordered is a signature item. Inductive Inductive

Valid – Logically correct conclusion

Valid conclusions Example: Sarah’s car will not start. If a car is out of gas, then it will not start. Sarah’s car is out of gas. Valid conclusion: Sarah’s car will not start.

Law of Detachment Law of Detachment: If is a true statement and p is true, the q is a true statement.

Conclusion: ED and EB are opposite rays. Determine whether each conclusion is valid based on the given information. If not, write invalid. Explain your reasoning. Given: If two angles form a linear pair, then their noncommon sides are opposite rays. Conclusion: ED and EB are opposite rays. Valid conclusion since the Conditional and hypothesis are true T ? T

Given: Mika goes to the beach, she will wear sunscreen. Determine whether each conclusion is valid based on the given information. If not, write invalid. Explain your reasoning. Given: Mika goes to the beach, she will wear sunscreen. Mika is wearing sunscreen. Conclusion: Mika is at the beach. Invalid since we Cannot determine whether The hypothesis is True or false. Mika could be at a ballgame ? T T

Conclusion: Points A, B, and C are noncollinear. Determine whether each conclusion is valid based on the given information. If not, write invalid. Explain your reasoning. Given: If three points are noncollinear, they determine a plane. Points A, B, and C lie in plane G. Conclusion: Points A, B, and C are noncollinear. Invalid, A,B, and C are in the plane, but that does not mean that they have to be noncollinear. T ? T

Conclusion: Felipe can go on the field trip. Determine whether each conclusion is valid based on the given information. If not, write invalid. Explain your reasoning. Given: if a student turns in a permission slip, then the student can go on the field trip. Felipe turned in his permission slip. Conclusion: Felipe can go on the field trip. Valid, law of detachment. T ? T

Venn Diagrams: Determine whether each conclusion is valid based on the given information. If not, write invalid. Explain using a Venn diagram. Given: If a primate is an ape, then it does not have a tail. Koko is a primate who does not have a tail. Conclusion: Koko is an ape Situation: primates can be apes (with tails) or primates without tails. If we know that Koko is a primate without a tail, can we conclude that Koko is an ape? Invalid

Conclusion: Figure A is a polygon. Venn Diagrams: Determine whether each conclusion is valid based on the given information. If not, write invalid. Explain using a Venn diagram. Given: if a figure is a square, then it is a polygon. Figure A is a square. Conclusion: Figure A is a polygon. Valid

Drawing conclusions If you get a job, then you will earn money. If you earn money, then you will buy a car. Valid conclusion: If you get a job, then you will buy a car.

Law of Syllogism Transitive property If p q and q r are true statements, then p r is a true statement. What property does Law of Syllogism resemble? Transitive property

Determine which statement follows logically from the given statements. If you do not get enough sleep, then you will be tired. If you are tired, then you will not do well on the test. If you are tired, then you will not get enough sleep. If you do not get enough sleep, then you will not do well on the test. If you do not do well on the test, the you did not get enough sleep. There is no valid conclusion.

Determine which statement follows logically from the given statements. If you like musicals, then you enjoy theater productions. If you are an actor, then you enjoy theater productions. If you are an actor, then you like musicals. If you like musicals, then you are an actor. If you do not enjoy musicals, then you are not an actor. There is no valid conclusion.

Determine which statement follows logically from the given statements. If Jamal finishes his homework, he will go out with his friends. If Jamal goes out with his friends, he will go to the movies. If Jamal goes out with his friends, then he finishes his homework. If Jamal finishes his homework, he will go to the movies. If Jamal does not go to the movies, he does not go out with his friends. There is no valid conclusion.

Draw a valid conclusion from the given statements, if possible Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning. Given: If you are 16 years old, then you can apply for a driver’s license. Nate is 16 years old. A valid Conclusion is Nate can apply For a driver’s license. Law of Detachment. T ? T

AM = MB by Law of Syllogism Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning. Given: The midpoint divides a segment into two congruent segments. If two segments are congruent, then their measures are equal. M is the midpoint of AB. AM = MB by Law of Syllogism

Draw a valid conclusion from the given statements, if possible Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning. If you interview for a job, then you wear a suit. If you interview for a job, then you will update your resume. No Valid Conclusion

Draw a valid conclusion from the given statements, if possible Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning. If it snows more than 5 inches, school will be closed. It snows 7 inches. Conclusion: School will be closed by Law of Detachment.