Foundations of Logic and Reasoning

Reasoning based on patterns you observe is called ____.

• Deductive Reasoning

• Inductive Reasoning

• Conjecture

• Counterexample

What are the next two terms in the following sequence?

5, 10, 20, 40, ...

• 60, 80

• 80, 160

• 65, 130

What are the next two terms in the following sequence?

1, -1, 2, -2, 3, -3, ...

• 3, -4

• 4, 5

• 4, -4

• -4, 4

What is the color of the 15th figure?

• Purple

• Red

• Teal

What shape would the 17th figure be?

• Circle

• Triangle

• Square

• Star

An example that shows a conjecture is incorrect is called ____.

• Deductive Reasoning

• Inductive Reasoning

• Conjecture

• Counterexample

What is a counterexample to the following conjecture?
 $\angle1\ and\ \angle2$  are supplementary, so one of the angles is acute.

•  $m\angle1=\ 120,\ m\angle2\ =\ 60$  

•  $m\angle1\ =\ 90\ =\ m\angle2$  

•  $m\angle1=100,\ m\angle2\ =\ 120$  

•  $m\angle1\ =\ 45,\ m\angle2\ =\ 135$  

What is a counterexample to the following conjecture?

When you multiply a number by 10, the product is divisible by 4.

• 3*10 = 30

• 4*10 = 40

• 6*10 = 60

• 10*10=100

Look for a pattern.

What are the next two terms in the sequence?

7, 14, 21, 28, ...

• 30, 35

• 34, 40

• 35, 42

• 42, 49

A conclusion you reach using inductive reasoning is called ____.

• Deductive Reasoning

• Inductive Reasoning

• Conjecture

• Counterexample