Conditional Statements and Types of Reasoning

REVIEW

February 21, 2023

Multiple Choice

Snakes are reptiles and reptiles are cold blooded. Therefore, snakes are cold blooded. 

• Deductive

• Inductive 

Multiple Choice

In the past, winter has always been cold in New York. Therefore, winter will be cold again this year.

• Deductive

• Inductive

Multiple Choice

Four out of five times, I beat Corey at pool and I'm going to play him tomorrow. So, I'll very likely win.

• Inductive

• Deductive

Conditional Statements

February 21, 2023

Objectives

• Transform a statement into an equivalent if- then statement.

• Determine the inverse, converse, and contrapositive of an if-then statement.

Some text here about the topic of discussion

Multiple Choice

What is the condition of the given statement below?

If you will get good grades, then I'll buy you an ice cream.

• You will get good grades.

• I'll buy you an ice cream.

Multiple Choice

What is the condition of the given statement?

• Jimmy will go to Orlando.

• Jimmy goes on vacation.

• Jimmy will go to Orlando.

• Who is Jimmy?

Multiple Choice

What is the consequence to the given statement?

• Clarkson will be the coolest.

• Clarkson will not be the coolest.

• Clarkson gives us Mountain Dew.

• Clarkson will not give us Mountain Dew.

Open Ended

How do you get the condition and the consequence of the given statement?

Conditional Statements

Def'n.:

A conditional statement is a statement that can be written as an if-then statement. That is, 

“If _(HYPOTHESIS/CONDITION)_, then _(CONCLUSION/CONSEQUENCE)_.”

Some text here about the topic of discussion

Multiple Choice

What is the hypothesis of this conditional?

• Sally goes to the park.

• Sally will fall off the swing.

• Parks don't have swings that Sally goes to.

• If Sally falls off the swing, she goes to the park.

Multiple Choice

What is the conclusion to the statement?

• You like fried chicken.

• You only like fried chicken from KFC.

• You like KFC.

• You hate KFC.

Conditional Statements

REWRITING:

Conditional statements can be put into an “if-then” form to clarify which part is the hypothesis and which is the conclusion.

​

Method: Turn the subject into a hypothesis. Turn the predicate into a conclusion.

Some text here about the topic of discussion

Multiple Choice

Rewrite the statement as a conditional statement.

"All dolphins are mammals."

• If a dolphin, then a mammal.

• If an animal is a dolphin, then it is a mammal.

• If an animal is a mammal, then it is a dolphin.

• If an animal is not a mammal, then it is not a dolphin.

Multiple Choice

Rewrite the statement as a conditional statement.

"Vertical angles are congruent."

• If vertical angles, then congruent.

• If two angles are vertical, then they are congruent.

• If two angles are cogruent, then they are vertical.

• If two angles are not vertical, then they are congruent.

Multiple Choice

Considering the statements below, what happened to the hypothesis and conclusion?

Statement 1: If two angles are vertical, then they are congruent.

Statement 2: If two angles are congruent, then they are vertical.

• switched

• negated

• interchanged and negated

Multiple Choice

Considering the statements below, what happened to the hypothesis and conclusion?

Statement 1: If two angles are vertical, then they are congruent.

Statement 2: If two angles are not vertical, then they are not congruent.

• switched

• negated

• interchanged and negated

Multiple Choice

Considering the statements below, what happened to the hypothesis and conclusion?

Statement 1: If two angles are vertical, then they are congruent.

Statement 2: If two angles are not congruent, then they are not vertical.

• switched

• negated

• interchanged and negated

Forms of Conditional Statements

Converse: Statement formed from a conditional statement by switching the hypothesis and conclusion.

​Inverse: Statement formed from a conditional statement by negating both the hypothesis and conclusion.

Contrapositive: Statement formed from a conditional statement by switching and negating both the hypothesis and conclusion.​​

Some text here about the topic of discussion

Multiple Choice

What is the converse to this statement?

• If it isn't dark outside, then it is not night.

• If it is night, then it is dark outside.

• If it is not night, then it is not dark outside.

• It is night.

Multiple Choice

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.

• If I do not have a Siberian Husky, then I do not have a dog.

• If I have a dog, then I have a Siberian Husky.

• If I do not have a dog, then I do not have a Siberian Husky.

• If I do not have a Siberian Husky, then I have a dog. 

Multiple Choice

Given, "If angles are congruent, then the measures of the angles are equal." Identify the contrapositive.

• If the measures of the angles are equal, then the angles are congruent.

• If angles are not congruent, then the measures of the angles are not equal.

• If the measures of the angles are not equal, then the angles are not congruent.

• If the angles are not congruent, then the measure of the angles are equal.

Open Ended

What is your takeaway from our discussion today?

Objectives

• Transform a statement into an equivalent if- then statement.

• Determine the inverse, converse, and contrapositive of an if-then statement.

Some text here about the topic of discussion