A-Level Mathematics · Proof · A4

Disproof by counterexample.

Disprove a universal mathematical claim by finding one valid counterexample.

A4 Proof8 MinutesAnimated lesson

WATCH THE IDEA MOVE

Animated
explanation.

Pause, replay and follow every logical step at your own pace.

01 / KEY IDEA

A universal claim says every case works; one case that fails is enough to disprove it.

02 / LEARNING OUTCOMES
  • Recognise universal statements
  • Test candidate examples
  • Present a decisive counterexample

WORKED EXAMPLE

Follow every
reason.

Disprove: every prime number is odd.

01

The claim applies to every prime number.

02

The number 2 is prime, because its only positive factors are 1 and 2.

03

But 2 is even, so it is a counterexample and the claim is false.

QUICK CHECK

Test the
logic.

Choose the statement that describes a valid mathematical proof.

What makes a mathematical proof valid?