Proof by counterexample (HSC SSCE Mathematics Extension 2): Quizzes
📚Quizzes
Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What is proof by counterexample used for?
What is proof by counterexample used for?
To disprove a statement
What does a 'for all' statement imply?
What does a 'for all' statement imply?
A property holds for all elements
Which number disproves 'All even numbers are divisible by 4'?
Which number disproves 'All even numbers are divisible by 4'?
6
What is a counterexample?
What is a counterexample?
An example that disproves a claim
Which number shows 'All prime numbers are odd' is false?
Which number shows 'All prime numbers are odd' is false?
2
What does the statement 'n^2 - n + 41 is prime' fail for?
What does the statement 'n^2 - n + 41 is prime' fail for?
n = 41
What is the role of counterexamples in mathematics?
What is the role of counterexamples in mathematics?
To refine general claims
What is a common counterexample for 'All whole numbers are positive'?
What is a common counterexample for 'All whole numbers are positive'?
0
What happens if a counterexample is found?
What happens if a counterexample is found?
The statement is proven false
What is the importance of modifying hypotheses?
What is the importance of modifying hypotheses?
To ensure they align with reality