Assertions of truth can usually be phrased in the form “if … then …”. Such assertions can be re-stated in many other equivalent ways. Doing so helps you to better understand these fundamental truths or to easily expose falsehoods.

Below are two infographics summarizing the main ways to re-phrase if-then statements. Click here for a PDF document that gives details (especially explaining what is meant by the word “implies”). The PDF also offers additional examples and in-class exercises.

This example is trivial to help make it clear that truth of one implies truth of all others (and untruth of one would also imply untruth of all others). But these sorts of rephrasings can give you unexpected insights when applied to nontrivial if-them statements. Try it on a few of the examples in the full PDF document!