UNIT 01 – LESSON 09 - DEDUCTIVE
REASONING
 ESSENTIAL QUESTION
 How can you use reasoning to solve problems?
 Scholars will
 Use the Law of Syllogism
 Use the Law of Detachment
WHAT IS 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.
INDUCTIVE VS. 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.
WHAT IS THE LAW OF DETACHMENT?
 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.
HOW DO YOU APPLY 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 figure is a square, then it is a parallelogram.
The figure is a parallelogram .
Conclusion: The figure is a square.
WHAT IS THE LAW OF SYLLOGISM?
 If hypothesis p, then conclusion q.
 If hypothesis q, then conclusion r.
 If hypothesis p, then conclusion r.
If these two statements are true,
then this statement is true.
Example
Given: 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.
HOW DO YOU APPLY THE LAW OF
SYLLOGISM?
Determine which statement follows logically from the given
statements.
(1) If Jamal finishes 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 finishes
his homework.
B - If Jamal finishes 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.