In proof by contradiction, we assume that the statement to be
proved is false. That is, we suppose the negation of the statement to
be proved to be true. Then, we show logically that our supposition
leads to a contradiction. Finally, we conclude that the statement to
be proved is true. This is because after a contradiction is reached, the
supposition is false therefore the statement to be proved is true.
The proof by contrapositive is based on the logical equivalence of a
statement and its contrapositive. To prove a statement by
contraposition, we take the contrapositive of the statement, prove
