2.3 Deductive Reasoning

Determine whether the stated conclusion is valid.
Given: If the sum of the measures of two angles is 180, then the angles are supplementary.
∠A and ∠B are supplementary.
Conclusion: The sum of the measure of two angles is 180

• The sum of the measures of two angles is 180
• Invalid
• ∠A and ∠B are supplementary.
• Valid

Determine whether the stated conclusion is valid.
Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments.
R is the midpoint of QS.
Conclusion: QR=RS

• Valid
• R is the midpoint
• Invalid
• A point is the midpoint of a segment.

Tags

CCSS.HSG.CO.C.9

CCSS.HSG.GPE.B.6

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 a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.

• Then it's not odd.
• Then it's a whole number.
• Then its square is divisible by 4
• Then it's even.

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

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

Tags

CCSS.HSA.SSE.A.1

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

Tags

CCSS.HSS.CP.B.6

Make a valid conclusion, if possible.

If you are a on diet, then you lose weight. Kelly lost weight.

• Kelly is on a diet.

• Kelly is sick.

• Kelly had surgery.

• No valid conclusion.

Make a valid conclusion, if possible.

If my cat is hungry, then she will meow. My cat is not hungry.

• My cat will not meow.

• My cat ate the couch.

• My cat will purr.

• No valid conclusion.

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