Laws of Logic Review

Laws of Logic Review

Law of Detachment

p→q

p

∴q

Conclusion is Valid

https://www.youtube.com/watch?v=kTSw3sKH0bo

Multiple Choice

If I go on vacation, then I won't do my work.

I went on vacation.

What is the logical conclusion?

• Therefore, I did my work.

• Therefore, I didn't do my work.

• Therefore, I didn't go on vacation.

• There is no logical conclusion.

Multiple Choice

If I go camping, then I need to pack my tent.

I went camping.

Therefore, I packed my tent.

Which law is being demonstrated?

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

• No law

Law of Syllogism

p→q

q→r

∴p→r

Conclusion is Valid

https://www.youtube.com/watch?v=blmq6ms0_es

Multiple Choice

If I see a black bear, then I will scream.

If I scream, then the bear will run away.

Therefore, if I see a black bear, it will run away.

Which law is being demonstrated?

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

• No law

Multiple Choice

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, therefore

• look out for the snowplows while driving to school.
• the big test will not be given today.
• the roads will be hard to drive on.
• you should call the school to see if school is canceled.

Multiple Choice

If you need help, then you stay after class.

If you stay after class, then you ask questions.

What is the logical conclusion?

• Therefore, if you stay after class, then you need help.

• Therefore, if you ask questions, then you need help.

• Therefore, if you need help, then you ask questions.

• There is no logical conclusion.

Law of Contrapositive

p→q

~q

∴~p

Conclusion is Valid

Multiple Choice

If I comb my hair, then I won't have tangles.

I have tangles.

Therefore, I didn't comb my hair.

Which law is being demonstrated?

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

• Error

Multiple Choice

If you go to the mall, then you will spend money.

You didn't spend any money today.

What is the logical conclusion?

• Therefore, you didn't go to the mall.

• Therefore, you don't have any money.

• Therefore, you went to the mall.

• There is no logical conclusion.

Inverse Error

p→q

~p

∴q

Conclusion is Invalid

No conclusion can be made

Multiple Choice

If you don't feel well, then you stay home.

You feel well.

What is the logical conclusion?

• Therefore, you stay home.

• Therefore, you don't stay home.

• Therefore, you don't feel well.

• There is no logical conclusion.

Converse Error

p→q

q

∴p

Conclusion is Invalid

No Conclusion can be made

Multiple Choice

If my team wins the game, then they will be the champions.

My team is the champion.

Therefore, my team won the game.

Which law is being demonstrated?

• Law of Detachment

• Law of Syllogism

• Inverse Error

• Converse Error

Multiple Choice

If I miss my bus, then I’ll be late for school.

I miss my bus.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

Multiple Choice

If a person is a librarian, then they read books.

If a person is a friend of Dana’s, then they read books.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

Multiple Choice

If this wind keeps up, then we will lose some trees.

We lose some trees.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

Syllogism Error

p→q

p→r

∴q→r or p→r

or

p→q

r→q

∴p→r or r→p

Conclusion is Invalid. No conclusion can be made

Multiple Choice

If I go to the movie, then I’ll eat popcorn.

If I eat popcorn, then I’ll enjoy the movie.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

Multiple Choice

Using deductive reasoning, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, then...

• Look out for the snowplows while driving to school.
• The big test will not be given today.
• The roads will be hard to drive on.
• You should call the school to see if school is canceled.

Multiple Choice

All bears are mammals, all mammals have kidneys; therefore all bears have kidneys. 

• Deductive
• Inductive

Multiple Choice

All chickens that we have seen have been brown; so, all chickens are brown. 

• Deductive
• Inductive

Multiple Choice

Using the Law of Syllogism, write a new conditional statement that follows from the pair of true statements.

If you study, then you will pass the test. If you pass the test, then you will pass the class.

• If you study, then you will pass the class.

• If you pass the test, then you should study.

• If you pass the class, then you will pass the test.

• If you study, then you will pass the test.

Multiple Choice

Using the Law of Detachment, draw a conclusion based on the statements given:

If a plane flies to China, then it will be a long flight. Sarah bought a ticket to China.

• Sarah will get stuck in the security line.

• Sarah will have a long flight.

• Sarah will need to bring a neck pillow and headphones.

• Sarah will get stuck with a middle seat on the plane.

Multiple Choice

Reasoning based on specific examples and patterns used to form conjectures is called ______________ reasoning.

• Inductive

• Deductive

Multiple Choice

Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.

• Inductive

• Deductive

Multiple Choice

(1) If you drive safely, then the life you save may be your own.
(2) AJ drives safely.
(3)  The life AJ saves may be his own.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Detachment
• Law of Syllogism
• Law of Contrapositive
• invalid

Multiple Choice

p→q
p
∴q
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Multiple Choice

p→q
q→r
∴p→r
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Multiple Choice

Which of the following is a biconditional statement?

• If you do not vote, then you are not at least 18 years old.
• You can vote if and only if you are 18 years old.
• If you are 18 years old, then you can vote.

Multiple Choice

Using the Laws of Logic, what is the conclusion based on the statements given:

If it is Friday, then Ms. Escamilla is happy.

If it is Friday, then Ms. McMillan is happy.

• Ms. Escamilla is happy

• Ms. McMillan is happy.

• Ms. Prose is happy.

• It is Friday

• No Conclusion

Multiple Choice

Using the Laws of Logic, what is the conclusion based on the statements given:

If Bella bakes cookies, then Aaron is happy.

Aaron isn't happy.

• Bella wasn't hungry

• Bella baked cookies

• Bella baked a cake

• Bella didn't bake cookies

• No Conclusion

Multiple Choice

Draw a conclusion from the statement.
If you are at least 25 year old, then you can rent a car.
You can rent a car

• You are at least 25 years old
• You can rent a car
• You can go on a road trip
• Invalid

Multiple Choice

Which law of logic is this:
If I buy a dress, then I won't get chips.
I bought a dress.
Therefore, I won't get chips.

• Law of Detachment
• Law of Contrapositive
• Law of Syllogism
• Law of Biconditional

Multiple Choice

Use the law of syllogism to draw a conclusion from the two given statements:
Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy

• You have more energy
• If you exercise regularly, then you have more energy
• You have a healthy body
• If you do not have a healthy body, then you do not exercise regularly

Multiple Choice

Draw a conclusion from the statement.
If Jack goes to school, then it is Monday.
Jack doesn't go to school.

• Jack skipped school.
• It isn't Monday.
• It's Saturday.
• Invalid

Multiple Choice

Draw a conclusion from the statement.
If a parasite lives in or on a host organism, then it harms its host.
A virus is a parasite.

• It will harm the host.
• I have a cold.
• It lives in or on a host
• Invalid

Multiple Choice

Using the law of contrapositive, write a new conditional statement given the following:

If the airport is crowded, then I will miss my flight.

I did not miss my flight.

• The airport was not crowded.

• The airport was crowded.

• Security was crowded.

• I took another flight.

Multiple Choice

Using the Law of Syllogism, write a new conditional statement that follows from the pair of true statements.

If you study, then you will pass the test. If you pass the test, then you will pass the class.

• If you study, then you will pass the class.

• If you pass the test, then you should study.

• If you pass the class, then you will pass the test.

• If you study, then you will pass the test.

Multiple Choice

Using the Law of Detachment, draw a conclusion based on the statements given:

If a plane flies to China, then it will be a long flight. Sarah bought a ticket to China.

• Sarah will get stuck in the security line.

• Sarah will have a long flight.

• Sarah will need to bring a neck pillow and headphones.

• Sarah will get stuck with a middle seat on the plane.

Multiple Choice

Used to prove that a conjecture is false.

• Counterexample
• Inductive Reasoning
• Concluding statement
• Conjecture

Multiple Select

How do you feel about the Laws of Logic now?

• Great! I am ready to take my test

• Ok. I need to study my notes a bit more before the test

• Not good. I need to practice more and maybe even come to Office Hours.