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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.
given: l is not parallel to m
all possibilities are considered and then all but one are proved false
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.
Assume the negation of the statement to be obtained.
Use the assumption to derive a contradiction.
Conclude that the original assumption is false. This last step establishes the truth of the statement to be obtained.
statement that is always true by logical structure