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

📚Flashcards
Disproof by Counter Example
Sign up to keep revising.Create a free account to study more flashcards and track your progress.

Practise the cards

10 cards from this deck

Show

Key idea of disproof by counterexample

One counterexample collapses an argument

How many counterexamples needed to disprove?

One

Words indicating a general statement to disprove

All, every, for every

Counterexample: multiples of 2 are multiples of 4

66 (multiple of 2, not 4)

Counterexample for 2n−12^n - 1 always prime (n≥2n \geq 2)

n=4n = 4

Value of 24−12^4 - 1

1515

Why 1515 disproves 2n−12^n - 1 always prime

15=5×315 = 5 \times 3 (not prime)

Counterexample: All prime numbers are odd

22

Why 22 disproves 'all primes are odd'

22 is prime and even

Is one counterexample sufficient?

Yes, one is enough to disprove

Explore AQA A-Level Mathematics Revision Notes by Topics

Explore AQA A-Level Mathematics Model Answers by Topics

Explore AQA A-Level Mathematics Quizzes by Topics

Explore AQA A-Level Mathematics Exam Questions by Topics

Join 100,000+ A-Level students studying Flashcards with us.

Select your subjects, and get access to A+ resources today.