Introducing the Contrapositive and Converse

  • Ulrich Daepp
  • Pamela Gorkin
Part of the Undergraduate Texts in Mathematics book series (UTM)


In the last chapter (see Theorem 2.7) we saw that two statement forms, P and Q, that have the same truth table are equivalent. This was also expressed by showing that the equivalence, PQ, is a tautology. When you are confronted with a mathematical statement that you need to prove, you will often find it helpful to paraphrase it. You will use tautologies to do so, since you don’t want to change the truth value of your statement. Some useful tautologies appeared in Theorem 2.9. More appear below and throughout this chapter.


Normal Subgroup Statement Form Original Statement Truth Table English Sentence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsBucknell UniversityLewisburgUSA

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