Reasoning & Proofs

Which law of logic is this?

If I clean the bathroom, then I don't have to do the dishes.

I cleaned the bathroom.

Therefore, I don't have to do the dishes.

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

• None

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

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.L.4.1C

CCSS.L.9-10.1B

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

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Use 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.

For any numbers a, b, and c, if a = b and b = c, then a = c.

• Transitive Property         
• Symmetric Property
• Reflexive Property
• Substitution Property

Tags

CCSS.7.EE.A.1

For any number a, a = a.

• Transitive Property         
                 
  
• Reflexive Property             
• Symmetric Property           
• Substitution Property

Tags

CCSS.7.EE.A.1

For any numbers a and b, if a = b, then b = a.

• Transitive Property         
• Reflexive Property 
• Symmetric Property   
• Substitution Property

Tags

CCSS.HSG.SRT.B.5

Name the property described
If CD = 4, then CD + 12 = 4 + 12

• Addition
• Subtraction
• Substitution
• Division

Tags

CCSS.7.EE.A.1

Then, AB = CD

• Definition of Congruence
• Definition of Midpoint
• Substitution Property

Tags

CCSS.8.G.A.2