# Geometry/Chapter 2/Lesson 2

## Introduction

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.

### Negation

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.

#### Examples

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 Inverse

• 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.

#### Examples

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.