Proofs and Logic: Unit 2

PROOFS

1

What goes FIRST in a proof?

The GIVEN!

2

What REASON would prove that ∠A ≅ ∠B ?

Definition of congruence

3

Which step of following Uno proof contains an error?

Statement

1. Yellow 7

2. Red 7

3. Red 5

4. Blue 4

5. Blue 6

STEP 4

4

What number card(s) can be used to correct the error in STEP 3 ? [NAME ALL THAT APPLY]

Statement

1. Red 8

2. Green 8

3. Blue 3

4. Blue 5

5. WILD

6. Red +2

Green 5 OR Blue 8

LOGICAL STATEMENTS

1

What type of statement is an "if-then"?

Conditional

2

What type of statement contains "if and only if" ?

Biconditional

3

Which statement is the inverse of the following conditional?

"If it is my birthday then there is cake."

▢ If it is NOT my birthday then there is NOT cake

▢ If there is NOT cake then it is NOT my birthday

▢ If there is cake then it is my birthday

If it is NOT my birthday then there is NOT cake

4

What is the contrapositive of the statement "If the angles are congruent, then they are vertical angles" ?

If they are NOT vertical angles then the angles are NOT congruent.

REASONING

1

What type of reasoning uses FACTS to make a conclusion?

Deductive Reasoning

(Think: Detective!)

2

What type of logic uses OBSERVATIONS and PATTERNS to make a conclusion?

Inductive Reasoning

(aka jumping to conclusions)

3

The statement "The sum of two 2-digit number is always a 3-digit number" is an example of what type of reasoning?

Inductive 

4

The statement "All oranges are fruits. All fruits grow on trees. Therefore, all oranges grow on trees" is an example of what type of reasoning?

Deductive 

COUNTEREXAMPLES

1

TRUE or FALSE: A counterexample proves that a statement is FALSE.

TRUE

2

Provide a counterexample to the statement:

The sky is always blue

- The sky is dark at night

-The sky is grey when it's rainy

- The sky is orange/pink/purple at sunset

3

Provide a counterexample to the statement:

"My students are always on time for class"

[INSERT TARDY STUDENT'S NAME HERE]

 lol

4

Provide a counterexample to the statement:

"Inception is the best Leonardo Dicaprio movie"

[INSERT LITERALLY ANY OTHER LEONARDO DICAPRIO MOVIE HERE]