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Contraposition is a logical operation that transforms a conditional statement into its equivalent contrapositive form. Learn how to use contraposition to prove or disprove statements, and see the law of contraposition and its applications in mathematics and logic.
In a proof of by contrapositive, you prove $P \to Q$ by assuming $\lnot Q$ and reasoning until you obtain $\lnot P$. In a "genuine" proof by contradiction, you assume both $P$ and $\lnot Q$, and deduce some other contradiction $R \land \lnot R$.
Learn how to use the contrapositive of a statement to prove its original form. The contrapositive of a statement is obtained by interchanging the hypotheses and conclusions and negating the whole statement.
Learn how to prove conjectures by using their contrapositives, which always have the same truth value as the original conjectures. See the formal definition, the steps to follow and some exercises with solutions.
Learn how to use proof by contrapositive, a method based on the equivalence of p ⇒ q and (not q) ⇒ (not p). See examples of how to apply this technique to claims about logic, kinship and irrational numbers.
Learn how to use proof by contradiction and proof by contraposition to establish statements that are not obvious from the definitions. See examples of these methods applied to theorems about thrackles, primes, and even numbers.
15 Ιουλ 2018 · Learn how to use the contrapositive method of proof in mathematics, with examples and exercises. The contrapositive of a statement is logically equivalent to the original statement and often easier to prove.
