Last updated on Oct 23, 2026

Disproof by Counter Example (Edexcel A-Level Mathematics): Quizzes

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Disproof by Counter Example

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How many counterexamples are needed to disprove a statement?

One

Which words often indicate a general statement that can be disproved by counterexample?

'All', 'every', 'for every'

What must a counterexample do to disprove a statement?

Not satisfy the statement

Which number disproves: 'All multiples of 2 are multiples of 4'?

$6$

Why does $6$ disprove 'All multiples of 2 are multiples of 4'?

$6$ is multiple of $2$ but not $4$

What value of $n$ disproves: ' $2^n - 1$ is always prime for $n \geq 2$ '?

$n = 4$

What is $15$ expressed as a product, showing it is not prime?

$15 = 5 \times 3$

Which number disproves: 'All prime numbers are odd'?

$2$

Why is $2$ considered a prime number?

Its only divisors are $1$ and $2$

After finding one counterexample, what can you conclude about the statement?

The statement is false

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