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Level 170

Indirect Proof


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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