Logic, Algebraic Properties of Equality and Proofs

What's the Property?

100

IF A=B, then B=A

What is the Symmetric Property of equality?

200

If A=B, then AxC=BxC

What is the Multiplication Property of equality? 

300

If A(B+C), then AB + AC

What is the Distributive Property?

400

If A=A, then A=A

What is the Reflexive Property of equality?

500

If A=B and B=C, then A=C

What is the Transitive Property of equality?

Name the Example

100

5x - 7 = 28

5x = 35 

What is the Addition Property of equality?

200

12 = x 

x = 12 

What is the Symmetric Property of Equality?

300

24 = 2x

12 = x

What is the division property of Equality?

400

3w + d = 22 and w =2 

then 6 + d = 22

What is the substitution property of equality?

500

WV = DE,  WV = 15 therefore  DE = 15 

What is the Transitive Property ?

Inductive or deductive?

100

1, 2, 3, 4, ... The next two numbers are...5,6

What is inductive reasoning?

200

The coin I pulled from a bag is a penny. The second coin pulled was also a penny. The last coin I pulled was a penny.  Therefore, all coins in the bag are pennies. 

What is the inductive?

300

All Raccoons are omnivores.  This animal is a racoon. Then this animal is an omnivore. 

What is deductive reasoning?

400

If I drive over the speed limit, then I will get a ticket.  I drove over the speed limit.  Therefore, I got the ticket

What is deductive reasoning? (Law of detachment)

500

A child examines ten tulip, all of which are red, and concludes that all tulips must be red. 

What is inductive reasoning?

Solving Proofs

100

Given: 4n - 2n = 4    Prove that n = 2

1. 4n - 2n = 4     1. Given 

2. 2n = 4            2. Combine Like Terms or Simplify 

3. n = 2              3. Division Property

200

Given: 7x - 9 = 54 Prove: x = 9 

1. 7x - 9 = 54        1. Given 

2. 7x = 63             2. Addition Property 

3. x = 9                3. Division Property 

300

Given: 4x - 12 = 20 Prove x = 8 

1. 4x - 12 = 20      1. Given 

2. 4x = 32             2. Addition Property 

3. x = 8                 3. Division Property 

400

Given: x = 14 and 3w - x = 58     Prove w = 24 

1. x = 14             1. Given 

2. 3w - x = 58      2. Given 

3. 3w - 14 = 58    3. Substitution Property 

4. 3w = 72           4. Addition Property 

5. w = 24            5. Division Property 

500

Given: 4(3x+12)=2x-28      Prove: x = 7.6

Statements:

1)4(3x+12)=2x-28,     1. Given 

2)12x+48=2x-28,        2. Distributive Property

3)10x=-76,                 3. Subtraction Property

4)x=-7.6                     4. Division Property

 

Miscellaneous

100

Every proof should start with this ....

What is it the given?

200

Hypothesis of if you have a library card, then you can check out books.

What is If you have a library card?

300

The converse of If it is Saturday, then there is no school.

What is If there is no school, then it is Saturday.

400

Inverse of If it is St. Patrick's Day, then it is March.

If it is not St. Patrick's Day, then it is not March. 

500

Angle A is congruent to Angle B 

Angle B is congruent to Angle C

The Transitive property states these two angles are congruent.

What is Angle A = Angle C?