Main content

## Geometry (FL B.E.S.T.)

### Unit 3: Lesson 3

Properties & definitions of transformations# Counterexamples | Lesson

## What is a counterexample?

A mathematical statement is a sentence that is either true or false.

A mathematical statement has two parts: a

**condition**and a**conclusion**.Showing that a mathematical statement is true requires a formal proof.

However, showing that a mathematical statement is false only requires finding one example where the statement isn't true. Such an example is called a

**counterexample**because it's an example that*counters*, or goes against, the statement's conclusion.### What skills are tested?

• Identifying a counterexample to a mathematical statement

## How can we identify counterexamples?

When identifying a counterexample, follow these steps:

- Identify the condition and conclusion of the statement.
- Eliminate choices that don't satisfy the statement's condition.
- For the remaining choices, counterexamples are those where the statement's conclusion isn't true.

## Your turn!

## Things to remember

A counterexample to a mathematical statement is an example that satisfies the statement's condition(s) but does not lead to the statement's conclusion.

Identifying counterexamples is a way to show that a mathematical statement is false.

When identifying a counterexample,

- Identify the condition and conclusion of the statement.
- Eliminate choices that don't satisfy the statement's condition.
- For the remaining choices, counterexamples are those where the statement's conclusion isn't true.

## Want to join the conversation?

- Does a counter example have to an equation or can we use words and sentences?(5 votes)
- You will need to use words to describe why the counter example you've chosen satisfies the "condition" (aka "hypothesis"), but does not satisfy the "conclusion"

Example: Tell whether the statement is True or False, then if it is false, find a counter example:

If a number is a rational number, then the number is positive.

Solution: This statement is false, -5 is a rational number but not positive.(3 votes)

- What grade math is this, because i'm going to 5 grade and I think this is for 9th graders.(3 votes)
- what is a counter exmple using 100 chart and adding one more or one less(2 votes)
- What would be a counterexample for this sentence? If a teacher likes math, then she is a math teacher.(2 votes)
- what is praxis core(1 vote)
- again how I would know this is a counterexample(0 votes)
- you would know if it is a counterexample because it makes the conditional statement false(4 votes)