Indirect Proof

The last kind of proof introduced in this course is a proof by contradiction, or it can be called an indirect proof.  This type of proof can be done using any of the forms previously discussed but it follows a specific pattern.  A proof by contradiction, or indirect proof, uses the negation of the statement to be proved and deductive reasoning to lead to a statement that can not be true, in other words, a contradiction.  A contradiction is when there are two statements that can not both be true.  This method of proof shows that all other possibilites are false, so the original conclusion has to be true. 

The following steps will be helpful when doing a proof by contradiction.

Step 1. State the negation of what you want to prove.

Step 2. Show that the negation leads to a contradiction.

Step 3. Conclude that the negation must have been false, therefore the original statement has to be true.

An indirect proof can use the method of your choice; paragraph, two-column, flow chart, etc.