Geometry - Law of Detachment

Determine whether the stated conclusion is valid.

Given: If an animal is a dog, then they like biscuits.

Sammy is a dog.

Conclusion: Sammy likes biscuits.

• Invalid

• Valid

• Sammy is a Great Dane

• Sammy is really a cat.

Draw a conclusion from the statement.

If you live in Orlando, then you live in Florida.

You live in Orlando.

• You live in Disney Land

• You are an old person.

• You live in Florida

• You live in Orlando

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

Draw a conclusion from the statement.

If you go fishing, then you will need to bring your fishing rod.

You go fishing.

• You will need to bring your fishing rod.

• Invalid

• You are a boring person.

• You are going to catch a fish.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Which law is modeled below?

p→q

p

∴q

• Law of Syllogism

• Law of Detachment

• Law of Contrapositive

• Law of Shannon

Use Law of Syllogism to make a conclusion.

If the perimeter of a square is 20 ft, then the length of a side is 5 ft.

If the length of a side of a square is 5 ft, then the area is 25 ft².

• If the side of a square is 5 ft, then the perimeter is 20 ft.

• If the perimeter of a square is 20 ft, then the area is 25 ft²

• If the area of a square is 25 ft², then the side length is 5 ft.

• If the are of a square is 25 ft², then the perimeter is 20 ft.

p→q
q→r
∴p→r
Which law is modeled?

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

If an angle is 40⁰, then it is acute.
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?

• ∠A is complementary to ∠B
• ∠A is acute.
• ∠A is obtuse.
• ∠A is 40⁰

Given the conditional statement;

"If it is Wednesday, then Jane doesn't have baseball practice."

What is the hypothesis of this statement.

• It is Wednesday

• Jane doesn't have baseball practice

• If it is Wednesday

• Then Jane doesn't have baseball practice

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Given the conditional;

"If Ty'Shawn is late then he will get a tardy"

What is the inverse?

• If Ty'Shawn is on time, then we won't get a tardy.

• If Ty'Shawn gets a tardy, then he is late.

• If Ty'Shawn is late then he won't get a tardy.

• If Ty'Shawn doesn't get a tardy, then he is on time.

Tags

CCSS.HSS.CP.A.1