Deductive Reasoning in Geometry

What is the main difference between deductive and inductive reasoning?

• Both are based on facts.

• Both are based on patterns.

• Deductive reasoning is based on facts, while inductive reasoning is based on patterns.

• Deductive reasoning is based on patterns, while inductive reasoning is based on facts.

Which famous fictional character is known for using deductive reasoning?

• Nancy Drew

• Miss Marple

• Hercule Poirot

• Sherlock Holmes

According to the Law of Detachment, if 'If P then Q' and 'P is true', what can be concluded?

• P is false

• Q is true

• Nothing can be concluded

• Q is false

If Allie scores 89 on her test and the condition is 'If Allie scores 85 or greater, she will earn an A', what can be concluded?

• Allie will fail

• Allie will earn an A

• Allie will earn a C

• Allie will earn a B

Using the Law of Detachment, if 'If it is winter, then Miss Johnson is cold' and 'Miss Johnson is cold', what can be concluded?

• It is definitely winter

• It is not winter

• Nothing can be concluded

• Miss Johnson is never cold

In the Law of Syllogism, if 'If P then Q' and 'If Q then R', what is the conclusion?

• If R then Q

• If Q then P

• If R then P

• If P then R

Using the Law of Syllogism, if 'If it is a holiday, then you do not have to go to school' and 'If it is Labor Day, then it is a holiday', what can be concluded?

• If it is a holiday, then it is Labor Day

• If it is Labor Day, then you do not have to go to school

• If you do not have to go to school, then it is Labor Day

• If you do not have to go to school, then it is a holiday

What can be concluded if 'If you are climbing a mountain at an altitude of 28,500 feet or higher, then you are on the tallest mountain above sea level' and 'You are on the tallest mountain above sea level'?

• You are on Mount Everest

• You are on a different mountain

• You are not on Mount Everest

• You are on a small hill

Combining the Laws of Detachment and Syllogism, if 'If you are climbing a mountain at an altitude of 28,500 feet or higher, then you are on Mount Everest' and 'You are climbing a mountain at an altitude of 28,500 feet or higher', what can be concluded?

• You are on a small hill

• You are not on Mount Everest

• You are on Mount Everest

• You are on a different mountain

If Martin walks his dog before dinner every day and Martin is now eating his dinner, what can be concluded?

• Martin has already walked his dog

• Martin will walk his dog tomorrow

• Martin has not walked his dog

• Martin is about to walk his dog