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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)
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)