Revision NotesExam QuestionsFlashcardsPast PapersMock Exams
IBMathsDPAnalysis & Approaches (AA)HLRevision Notes1. Number & AlgebraSimple Proof & ReasoningDisproof by Counter Example

Disproof by Counter Example (DP IB Analysis & Approaches (AA)): Revision Note

Amber

Written by: Amber

Reviewed by: Mark Curtis

Updated on

DP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SL

Disproof by counterexample

What is disproof by counterexample?

  • Disproof by counterexample means proving a result (statement) is not true

    • by finding an example that fails

      • This is called a counterexample

  • You only need to find one counterexample to disprove the statement

  • To help find the counterexample, try unusual numbers

    • For example

      • 0 or 1

      • 2 (being the only even prime)

      • square root of 2 or pi (being irrational)

      • negative numbers

Examiner Tips and Tricks

It is not enough to just write down the counterexample - you need to show why it does not work!

Worked Example

Disprove the following statements by means of a counterexample.

(a) Given that n element of straight integer numbers to the power of plus, if n squared is a multiple of 4, then n is also a multiple of 4.

1-4-1-ib-aa-hl-disproof-by-counter-example-we-i

(b) Given that x element of straight integer numbers then 3 x is always greater than 2 x.

1-4-1-ib-aa-hl-disproof-by-counter-example-we-ii

You've read 0 of your 5 free revision notes this week

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Test yourself
    Previous:Proof by DeductionNext:Proof by Induction
    Author
    Reviewer
    Amber

    Author: Amber

    Expertise: Maths Content Creator

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

    Mark Curtis

    Reviewer: Mark Curtis

    Expertise: Maths Content Creator

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.