2.4 Deductive Reasoning

Essential Vocabulary• Deductive reasoning - is the process

of reasoning logically from given statements to a conclusion

• Law of detachment – if a conditional is true and its hypotenuse is true, then its conclusion is true

• Law of Syllogism - If p→q and q →r are true statements then p→r is a true statement.

The car being worked on will not start.

A gardener knows that if it rains, the garden will be watered.

It is raining. What can we conclude?

The garden will be watered.

If a student wants to go to college, then the student must study hard.

Rashid wants to go to University of North Carolina. What can we conclude?

Rashid must study hard.

If there is lightning, then it is not safe to be out in the open.

Maria sees lightning from the soccer field. What can we conclude?

She is not safe.

If a road is icy, then driving conditions are hazardous.

Driving conditions are hazardous. What can we conclude?

It is not possible to conclude anything.

If you read a good book, then your time is spent well.

If you are studying biology, then you are studying a science.If you are studying botany, then you are studying biology.

If you are studying botany, then you are studying a science.

If an animal is a red wolf, then its scientific name is Canis rufus.If an animal is names Canis rufus, then it is endangered.

If an animal is a red wolf, then it is endangered.

If a river is more than 4000 miles long, then it is longer than the Amazon.If a river is longer than the Amazon, then it is the longest river in the world.

The Nile is 4132 miles long. What can we conclude?

If a river is more than 4000 miles long then it is the longest river in the world.

The Nile is the longest river in the world.

16. Must be true; E,A,D17. Must be true; E,A,C18. May be true; EA don’t know19. Not true: EAC20. May be true; E21. Not true; AED