Conditional Reasoning: Counterexamples and Case Analysis

Methods in this video

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1. 1

   List every case, find a counterexample

   ▶ 0:58

   When to use it: Someone says "must", "will" or "can't both", or the question asks which statement must be true; the rules in the box don't fix the result: matches are still to be played, the season's scores aren't given, or which two days of the week isn't said.

   • "Must": every case has to work. One counterexample proves it wrong; only if every case works is it right.
   • "Could": one case that works is enough.
   • List every case first: the remaining matches, all the days, in order, missing none; a counterexample must keep every rule in the box.
2. 2

   List every route and every hurdle, one by one

   ▶ 6:38

   When to use it: The box lists several ways in (There are three ways to qualify, either … or) or several conditions that must all be met (must … must also, Additionally, even if …); someone says "our only chance", "as long as …" or "could", or someone didn't make it and the question is which condition stopped them.

   • List the routes and hurdles in the box one by one, and number them.
   • Routes (OR): one route is enough. When someone says "only", look for another route.
   • Hurdles (AND): clear every one. Clearing one ≠ must; miss one, and even "could" is wrong; not tested yet ≠ failed.
   • If someone can't go, check the hurdles one by one to find which one stopped them.