In mathematics, proof by contrapositive, or proof by contraposition, is a rule of inference used in proofs, where one infers a conditional statement from its contrapositive. In other words, the conclusion "if A, then B" is inferred by constructing a proof of the claim "if not B, then not A" instead.
How do you prove by contradiction?
The steps taken for a proof by contradiction (also called indirect proof) are:
- Assume the opposite of your conclusion. ...
- Use the assumption to derive new consequences until one is the opposite of your premise. ...
- Conclude that the assumption must be false and that its opposite (your original conclusion) must be true.
Which is easier direct proof or proof by contraposition?
used to prove conditional statements of the form “If P, then Q.” Although it is possible to use direct proof exclusively, there are occasions where contrapositive proof is much easier. To understand how contrapositive proof works, imagine that you need to prove a proposition of the following form.
