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indirect proof or proof by contradiction

A proof in which you prove that a statement is true by first assuming that its opposite is true. If this assumption leads to an impossibility, then you have proved that the original statement is true.

Example

given: l is not parallel to m

inderect reasoning

all possibilities are considered and then all but one are proved false

inderect proof

a proof invovling indirect reasoning

Law of excluded middle

A statement is either true or false.

Law of contradiction

A statement and its negation cannot both be true.

Law of elimination.

When all possibilities have been shown to be false, the remaining possibility must have been true.

Step 1

Assume the negation of the statement to be obtained.

Step 2

Use the assumption to derive a contradiction.

Step 3

Conclude that the original assumption is false. This last step establishes the truth of the statement to be obtained.

Tautology

statement that is always true by logical structure