## IntroductionEdit

Now that we know about conditional statements and what makes up one—now, we will move on to mixing these statements around! This lesson, we will be learning about the **converse** and the **inverse** of a conditional statement. Next lesson (Geometry/Chapter 2/Lesson 3), we will go over the contrapositive of a statement, biconditional statements, and logic symbols.

### NegationEdit

Before we jump into the converses and inverses of conditional statements, we must introduce the topic of **negation** to you. The negation of a conditional statement is the *complete opposite* of the original conditional statement. If the original statement is already negative, the negation would be the *positive* form of the statement.

#### ExamplesEdit

- Statement 1: The dog is barking
- Statement 2: The dog is
*not*barking

- Statement 1: The cats are
*not*loud - Statement 2: That cats are loud

- Statement 1: You are allowed to touch the sandwich.
- Statement 2: You are
*not*allowed to touch the sandwich.

### Converse and InverseEdit

**Converse**- The opposite (in terms of placement) of the given conditional statement.**Inverse**- The negation of the hypothesis and conclusion.

This is a fairly easy section of this lesson, so we will stop right here and move on to the examples.

#### ExamplesEdit

**Statement**: If the ball is red, then it is my ball.**Converse**: If it is my ball, then it is red.**Inverse**: If the ball is not red, then it is not my ball.

**Statement**: If the pie is tasty, then my mom cooked it.**Converse**: If my mom cooked it, then the pie is tasty.**Inverse**: If the pie is not tasty, then my mom did not cook it. [change in grammar]

**Statement**: If the bamboo did not fly, I would have taken it.**Converse**: If I would have taken it, then the bamboo did not fly.**Inverse**: If the bamboo did fly, I would not have taken it.