2.1. Conjectures and Counterexamples http://www.ck12.org
2.1 Conjectures and Counterexamples
Here you’ll learn how to make educated guesses, or conjectures, based on patterns. You’ll also learn how to disprove
conjectures with counterexamples.
What if your older brother told you that all of his male friends at school play sports, so all guys must play sports.
How could you prove him wrong? After completing this Concept, you will be able to make conjectures and disprove
conjectures using counterexamples.
Watch This
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URL: http://www.ck12.org/flx/render/embeddedobject/52467CK-12 Foundation: Chapter2ConjecturesandCounterexamplesA
Watch the final part of this video.
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URL: http://www.ck12.org/flx/render/embeddedobject/1373James Sousa: Counterexamples
Guidance
Aconjectureis an “educated guess” that is based on examples in a pattern. Numerous examples may make you
believe a conjecture. However, no number of examples can actuallyprovea conjecture. It is always possible that the
next example would show that the conjecture is false. Acounterexampleis an example that disproves a conjecture.
Example A
Here’s an algebraic equation and a table of values fornand with the result fort.
t= (n− 1 )(n− 2 )(n− 3 )