Converse, Inverse, & Contrapositive

​A) Conditional Statements

"If..., then..."

B) Hypothesis comes after "if"

C) Conclusion comes after "then"

D) Converse

• The hypothesis and conclusion switch order.

E) Inverse

• The conditional statement becomes opposite.

Multiple Choice

What kind of statement is the following?

"If you make a lot of money, then you can buy a nice car."

• Contrapositive Statement

• Converse Statement

• Conditional Statement

• Controversial Statement

Multiple Choice

"If you make a lot of money, then you can buy a nice car."

What is the hypothesis?

• You can't buy a nice car.

• You make a lot of money.

• You can buy a nice car.

• You don't make a lot of money.

Multiple Choice

"If you make a lot of money, then you can buy a nice car."

What is the conclusion?

• You can't buy a nice car.

• You make a lot of money.

• You can buy a nice car.

• You don't make a lot of money.

Multiple Choice

What would be the converse of the conditional statement?

"If you make a lot of money, then you can buy a nice car."

• If you can't buy a nice car, then you don't make a lot of money.

• If you don't make a lot of money, then you can't buy a nice car.

• If you can buy a nice car, then you make a lot of money.

• If you make a lot of money, then you can buy a nice car.

Multiple Choice

What would be the inverse of the conditional statement?

"If you make a lot of money, then you can buy a nice car."

• If you can't buy a nice car, then you don't make a lot of money.

• If you don't make a lot of money, then you can't buy a nice car.

• If you can buy a nice car, then you make a lot of money.

• If you make a lot of money, then you can buy a nice car.

Contrapositive

• The conditional statement is both converse AND inverse.

For Example

Conditional Statement "If I'm old, then I'm wise."

Contrapositive "If I'm not wise, then I'm not old."

Multiple Choice

What would be the contrapositive of the conditional statement?

"If you make a lot of money, then you can buy a nice car."

• If you can't buy a nice car, then you don't make a lot of money.

• If you don't make a lot of money, then you can't buy a nice car.

• If you can buy a nice car, then you make a lot of money.

• If you make a lot of money, then you can buy a nice car.

Open Ended

The contrapositive is both the converse and inverse of a conditional statement. Type the contrapositive for the following statement:

"If I'm sleepy, then I'm lazy."

Multiple Choice

Conditional Statement

“If I live in Los Angeles, then I live in California.”

What is the p?

• I don't live in California

• I live in California

• I don't live in Los Angeles

• I live in Los Angeles

Multiple Choice

Conditional Statement

“If I live in Los Angeles, then I live in California.”

What is the q?

• I don't live in California

• I live in California

• I don't live in Los Angeles

• I live in Los Angeles

Multiple Choice

Conditional Statement

“If I live in Los Angeles, then I live in California.”

What is the ~p?

• I don't live in California

• I live in California

• I don't live in Los Angeles

• I live in Los Angeles

Multiple Choice

Conditional Statement

“If I live in Los Angeles, then I live in California.”

What is the ~q?

• I don't live in California

• I live in California

• I don't live in Los Angeles

• I live in Los Angeles

Multiple Choice

Conditional Statement $$p\ \rightarrow\ q$$

What is the converse?

• $$\sim q\ \rightarrow\ \sim p$$

• 
  $$q\ \rightarrow\ p$$

• $$\sim p\ \rightarrow\ \sim q$$

Multiple Choice

Conditional Statement $$p\ \rightarrow\ q$$

What is the inverse?

• $$\sim q\ \rightarrow\ \sim p$$

• 
  $$q\ \rightarrow\ p$$

• $$\sim p\ \rightarrow\ \sim q$$

Multiple Choice

Conditional Statement $$p\ \rightarrow\ q$$

What is the contrapositive?

• $$\sim q\ \rightarrow\ \sim p$$

• 
  $$q\ \rightarrow\ p$$

• $$\sim p\ \rightarrow\ \sim q$$