Disproof by Counter Example (AQA A-Level Mathematics): Flashcards
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Practise the cards
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Key idea of disproof by counterexample
Key idea of disproof by counterexample
One counterexample collapses an argument
How many counterexamples needed to disprove?
How many counterexamples needed to disprove?
One
Words indicating a general statement to disprove
Words indicating a general statement to disprove
All, every, for every
Counterexample: multiples of 2 are multiples of 4
Counterexample: multiples of 2 are multiples of 4
(multiple of 2, not 4)
Counterexample for always prime ()
Counterexample for always prime ()
Value of
Value of
Why disproves always prime
Why disproves always prime
(not prime)
Counterexample: All prime numbers are odd
Counterexample: All prime numbers are odd
Why disproves 'all primes are odd'
Why disproves 'all primes are odd'
is prime and even
Is one counterexample sufficient?
Is one counterexample sufficient?
Yes, one is enough to disprove
