Chapter 2
Section 2.3
Apply Deductive Reasoning
Deductive Reasoning

Uses facts, definitions, accepted
properties, and the laws of logic to form
a logical argument.

Inductive Reasoning – uses specific
examples and patterns to form a
conjecture.
Law of Detachment
1.) If p, then q
2.) p
3.) q
Example – Law of Detachment
1.) If Joe is a student at RBR, then Joe has
an ID number.
2.) Joe is a student at RBR.
3.) Joe has an ID number.

Law of Detachment
1.) If you plan on attending Princeton, then you
need to be in the top 5% of your class.
2.) Jaime plans on attending Princeton.
3.) Jaime needs to be in the top 5% of her
class.
Does the Law of Detachment
Apply?
1.) If a dog eats Dogfood Delights, then the
dog is happy.
2.) Fido is a happy dog.
3.) NO CONCLUSION.
Does the Law of Detachment
Apply?
1.) If Fonzo is a fish, then he can swim.
2.) Fonzo can swim.
3.) NO CONCLUSION.
Can you draw a valid conclusion from the two
statements using the Law of Detachment?
1.) If the class is long and boring, then a student
in the class is likely to day dream.
2.) John day dreams in science class.
Can you draw a conclusion? No Conclusion
1.) If you want good health, then you should eat
vegetables and fruits everyday.
2.) Jackie wants good health.
Can you draw a conclusion?
Yes. Jackie should eat
vegetables and fruits every day.
The Law of Syllogism
1.) If p, then q.
2.) If q, then r.
3.) If p, then r.
Law of Syllogism Example:
1.) If you were born in Mexico, then you were
born in North America.
2.) If you were born in North America, then you
were born in the western hemisphere.
3.) If you were born in Mexico, then you were
born in the western hemisphere.
Law of Syllogism Example
1.) If you drive a car, then you have a
license.
2.) If you have a license, then you
passed your driver’s test.
3.) If you drive a car, then you passed
your driver’s test.
Can a valid conclusion be made from statements 1
and 2? Write statement three if it applies.
1.) If the team wins, then we will celebrate.
2.) If we celebrate, then we will be out late.
3.) If the team wins, then we will be out late.
1.) If two angles are vertical, then they do not form a
linear pair.
2.) If two angles are vertical, then they are
congruent.
3.) No, the law of syllogism does not apply.
Determine if the law of detachment,
law of syllogism or neither apply.
1.) If you drive safely, then the life you save may
be your own.
2.) Sean drives safely.
3.) The life he saves may be his own.
Law of Detachment Applies
1.) If two angles are right, then they are congruent.
2.) A ≡ B
3.) A and B are right angles.
None Apply