2.2 Deductive Reasoning and Logic Laws

Is the conclusion based on inductive or deductive reasoning?

Students at Olivia’s high school must have a B average in order to participate in sports. Olivia has a B average, so she concludes that she can participate in sports at school.

• inducutive

• deductive

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

All observed houses on South Street have roofs that are falling apart.  Sherry lives on South Street.  Her roof is falling apart. 

• Deductive
• Inductive

Tags

CCSS.L.1.1D

CCSS.L.3.1A

Use the Law of Syllogism to make a conclusion.  If a number is divisible by 10, then it is divisible by 2.  If a number is divisible by 2, then it is even.

• If a number is divisible by 10, then it is even,
• If a number is even, then it is divisible by 10.
• If a number is divisible by 2, then it is even.
• If a number is even, then it is divisible by 2.

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.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3)  ???????
What belongs in line 3?

• Figure A is a polygon.
• Figure A is a circle.
• Figure A is a square.
• invalid; nothing belongs in line 3

Tags

CCSS.2.G.A.1

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

• No law

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.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

If the binding of the book is broken, then the student will have to pay for a new one. Michael has to pay for a new book, so he concludes the binding on his book is broken. Is he correct?

• Yes
• No

Tags

CCSS.RI.11-12.2

CCSS.RI.8.1

CCSS.RI.9-10.1

CCSS.RL.8.1

CCSS.RL.9-10.1

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

(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