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

Disproof by Counter Example

What is disproof by counter-example?

• Disproving a result involves finding a value that does not work in the result

• That value is called a counter-example

How do I disprove a result?

• You only need to find one value that does not work

• Look out for the set of numbers for which the statement is made, it will often be just integers or natural numbers

• Numbers that have unusual results are often involved

  • It is often a good idea to try the values 0 and 1 first as they often behave in different ways to other numbers

  • The number 2 also behaves differently to other even numbers

    • It is the only even prime number

    • It is the only number that satisfies 

  • If it is the set of real numbers consider how rational and irrational numbers behave differently

  • Think about how positive and negative numbers behave differently

    • Particularly when working with inequalities