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 09 - DEDUCTIVE REASONING

Deductive reasoning using facts, definitions, accepted properties, and the laws of logic to form a logical argument.

This is different from inductive reasoning, which using specific examples and pattern to form a conjecture.

WHAT IS DEDUCTIVE REASONING?

WEATHER Determine whether the 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.

INDUCTIVE VS. DEDUCTIVE REASONING

Determine whether the 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 not be cold tomorrow morning.

INDUCTIVE VS. DEDUCTIVE REASONING

If the hypothesis of a true conditional statement is true, then the conclusion is also true.

If p q is true statement, and p is true, then q is true. Example – 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.

WHAT IS THE LAW OF DETACHMENT?

Determine whether the conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.

Given: If a fi gure is a square, then it is a parallelogram. The fi gure is a parallelogram.

Conclusion: The fi gure is a square.

HOW DO YOU APPLY THE LAW OF DETACHMENT?

If hypothesis p, then conclusion q. If hypothesis q, then conclusion r. If hypothesis p, then conclusion r.

ExampleGiven: 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.

WHAT IS THE LAW OF SYLLOGISM?

If these two statements are true,

then this statement is true.

Determine which statement follows logically from the given statements.

(1) If Jamal fi nishes his homework, he will go out with his friends.(2) If Jamal goes out with his friends, he will go to the movies.

A - If Jamal goes out with his friends, then he fi nishes his homework.B - If Jamal fi nishes his homework, he will go to the movies.C - If Jamal does not go to the movies, he does not go out with his friends.D - There is no valid conclusion.

HOW DO YOU APPLY THE LAW OF SYLLOGISM?