What is contraduction method
Dear student,
Assuming your question to be as follows :
Sometimes, when it is difficult or downright impossible to prove the truth of a statement directly, we may turn to proof by contradiction. We know that a statement cannot both be true and false - it has to be one or the other.
Proof by contradiction uses this fact to prove something is true by showing that it cannot be false. When proving something is true using proof by contradiction, you assume the statement to be false, and as you proceed with the proof, you run into a contradiction, making the assumption of your original statement being false impossible, thus it must be true.
Assuming your question to be as follows :
Sometimes, when it is difficult or downright impossible to prove the truth of a statement directly, we may turn to proof by contradiction. We know that a statement cannot both be true and false - it has to be one or the other.
Proof by contradiction uses this fact to prove something is true by showing that it cannot be false. When proving something is true using proof by contradiction, you assume the statement to be false, and as you proceed with the proof, you run into a contradiction, making the assumption of your original statement being false impossible, thus it must be true.
When using proof by contradiction, we follow these steps.
- Assume your statement to be false.
- Proceed as you would with a direct proof.
- Come across a contradiction.
- State that because of the contradiction, it can't be the case that the statement is false, so it must be true.