Conditional statements

​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."

​(contrapostive) ~q -> ~p

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?

• $$\sim q\ \rightarrow\ \sim p$$

• 
  $$q\ \rightarrow\ p$$

• $$\sim p\ \rightarrow\ \sim q$$

Multiple Choice

What is the contrapositive to this?

• If an angle is not greater than 90, then it is not obtuse

• If an angle is not obtuse then it is not greater than 90.

• If an angle is 90, then it is right

• If an angle is not greater than 90 then it must be acute

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

When taking the converse we ___________ the hypothesis and conclusion.

• negate
• switch
• leave the same
• switch and negate

Multiple Choice

What is the inverse?

If a number can be divided by 2, then it is even.

• If a number cannot be divided by 2, then it is not even.

• If a number is not even, then it cannot be divided by 2

• If a number can be divided by 2, then it is odd

• If a number is even, then it can be divided by 2.

Multiple Choice

What is the inverse of this statement?

• If 2 lines are not parallel, then they touch

• If 2 lines touch, then they are not parallel

• If 2 lines are parallel, then they touch

• If 2 lines are not parallel, then they are not lines.

Multiple Choice

What is the contrapositive to this?

• If the food is not cooked, then it is not in the oven.

• If the food is not in the oven, then it is not cooked.

• If the food is cooked, then its in the oven.

• If food is not in the oven, then its cooked.

Multiple Choice

Which is the converse of the statement?

• If you are not a guitar player, then you are not a musician.

• If you are a musician, then you are a guitar player.

• If you are a guitar player, then you are not a musician.

• If you are not a musician, then you are not a guitar player.

Match

Match the following

• $$\sim p\rightarrow\sim q$$  

• $$q\rightarrow p$$  

• $$p\rightarrow q$$  

• $$\sim q\rightarrow\sim p$$  

Inverse

Converse

Original Conditional

Contrapositive

• Inverse

• Converse

• Original Conditional

• Contrapositive

Multiple Choice

Every Wednesday is an early release day.

Right this as a conditional statement.

• If it is an early release day, then its wednesday.

• If it is Wednesday then it is an early release day.

• It is Wednesday if and only if its an early release day.

• It is an early release day if and only if its Wednesday.

Multiple Choice

A square is a rectangle.

Write this as a conditional statement.

• If it is a square then it is a rectangle.

• If it is a rectangle then it is a square.