2.4 deductive reasoning. essential vocabulary deductive reasoning - is the process of reasoning...
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2.4 Deductive Reasoning
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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.
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The car being worked on will not start.
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A gardener knows that if it rains, the garden will be watered.
It is raining. What can we conclude?
The garden will be watered.
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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.
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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.
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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.
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If you read a good book, then your time is spent well.
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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.
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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.
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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.
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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