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

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Disproof by Counter Example
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Effect of one counterexample on an argument

Collapses/disproves it

No. of counterexamples needed to disprove a statement

One

Type of statement disproved by counterexample

General statements (using 'all', 'every', 'for every')

First step in disproof by counterexample method

Understand the statement

What to find to disprove a statement

One example that does NOT satisfy the statement

Counterexample: multiple of 2 but not 4

66

Value of 24−12^4 - 1

1515

Why 1515 is not prime

15=5imes315 = 5 imes 3 (composite)

Statement: 2n−12^n - 1 always prime for ngeq2n geq 2

False, counterexample: n=4n=4 gives 1515 (not prime)

Counterexample to 'all prime numbers are odd'

22 (prime but even)

Why 22 is a prime number

Only divisors are 11 and 22

After finding a counterexample, what to conclude

The statement is false

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