2.4 Deductive Reasoning

p → q
q → r
∴ p → r
Which law is modeled?

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

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, then the big test will not be given today.
If 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.

Using the Law of Syllogism, which of these is a valid conclusion from the following pair of true statements.

If the sun is shining, then it is a beautiful day.

If the sun is shining, then we will have a picnic.

• If we have a picnic, then the sun is shining.

• If it is a beautiful day, then the sun is shining.

• If it is a beautiful day then we will have a picnic.

• There is no valid conclusion.

If a figure is a square, then it is a rectangle. If a figure is a rectangle, then it has 4 right angles.

What can you conclude?

• If a figure has 4 right angles, then it is a square.

• If a figure is a square, then it has 4 right angles.

• Nothing

• If a figure is a rectangle, then it is a square with 4 right angles.

Tags

CCSS.HSG.CO.C.11

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

• If Tom goes fishing then he catches a fish.
• If Tom brings his pole then he goes fishing
•  If Tom catches a fish then he brought his pole.
• If Tom brings his pole then he catches a fish.

Using the Law of Detachment, what can you conclude?
If you earn more than $14, then you can buy a new CD.
You earn $15.

• you can buy a new CD
• you cannot buy a new CD
• no conclusion can be made
• you earn more than $14

p → q
p
∴ q
Which law is modeled?

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

Draw a conclusion from the statement.
Given: If you live in Orlando, then you live in Florida.
Roger lives in Orlando.
Conclusion: ?

• Roger lives in Disney Land
• Roger is an old person.
• Roger lives in Florida
• Roger lives in Orlando

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.1

CCSS.RI.8.8

Is the stated conclusion valid or invalid?

Statements: If it is Monday, then Jack goes to school. Jack goes to school.

Conclusion: It is Monday.

• The conclusion is VALID (true)

• The conclusion is INVALID (not necessarily true)

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.1

CCSS.RI.8.8

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