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In logic, the contrapositive of a conditional statement is formed by negating both terms and reversing the direction of inference. Explicitly, the contrapositive of the statement "if A, then B" is "if not B, then not A." A statement and its contrapositive are logically equivalent: if the statement is true, then its contrapositive is true, and vice versa.〔Regents Exam Prep, (contrapositive ) definition〕 In mathematics, proof by contraposition is a rule of inference used in proofs. This rule infers a conditional statement from its contrapositive.〔(Larry Cusick's (CSU-Fresno) How to write proofs tutorial )〕 In other words, the conclusion "if A, then B" is drawn from the single premise "if not B, then not A." ==Example== Let ''x'' be an integer. :To prove: ''If ''x''² is even, then ''x'' is even. Although a direct proof can be given, we choose to prove this statement by contraposition. The contrapositive of the above statement is: :''If ''x'' is not even, then ''x''² is not even. This latter statement can be proven as follows. Suppose ''x'' is not even. Then ''x'' is odd. The product of two odd numbers is odd, hence ''x''² = ''x''·''x'' is odd. Thus ''x''² is not even. Having proved the contrapositive, we infer the original statement.〔 (p. 50).〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「proof by contrapositive」の詳細全文を読む スポンサード リンク
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