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Course: Geometry (FL B.E.S.T.) > Unit 3
Lesson 3: Properties & definitions of transformationsCounterexamples | 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.(5 votes)
- What grade math is this, because i'm going to 5 grade and I think this is for 9th graders.(5 votes)
- what is a counter exmple using 100 chart and adding one more or one less(2 votes)
- If multiplication is to make more of, why does it not apply to money when we square 1 pound? But applies to other digits.
For example 100 pennies = 1 pound but when you square both sides of the equation, it becomes counterexample of the statemant of 100 pennies = 1 pound because now, 10,000 pennies = 1 pounds(1 vote) - What would be a counterexample for this sentence? If a teacher likes math, then she is a math teacher.(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)