1. Apply Deductive Reasoning
Chapter 2 Section 2.3
Apply Deductive Reasoning

2. 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.

3. Law of Detachment
1.) If p, then q
2.) p
3.) q

4. 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.

5. 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.

6. 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.

7. Does the Law of Detachment Apply?
1.) If Fonzo is a fish, then he can swim.
2.) Fonzo can swim.
3.) NO CONCLUSION.

8. 2.) John day dreams in science class. Can you draw a 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?
1.) If you want good health, then you should eat vegetables and fruits everyday.
2.) Jackie wants good health.
No Conclusion
Yes. Jackie should eat vegetables and fruits every day.

9. The Law of Syllogism 1.) If p, then q. 2.) If q, then r.
3.) If p, then r.

10. 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.

11. 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.

12. Can a valid conclusion be made from statements 1 and 2
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.

13. 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.
1.) If two angles are right, then they are congruent.
2.) A ≡ B
3.) A and B are right angles.
Law of Detachment Applies
None Apply