Every even number is not prime. The number \(9\) is not an even number, therefore it is not not prime, i.e: the number \(9\) is prime.
In a school there are three sports clubs, which we call \(A\), \(B\), and \(C\).
A student argues as follows:
“To find how many people attend at least one club, we can add the number of people in each club. However, students who attend all three clubs get counted three times. To fix this, we should subtract them twice. Therefore, the number of people who attend at least one club is \[\text{people in }A+\text{people in }B+\text{people in }C -2\times(\text{people in all three clubs}).\]”
Is this reasoning correct?
Everyone makes mistakes in maths — and that’s a good thing! Mistakes help us understand what really works and what doesn’t.
The more mistakes you see, the easier they become to spot. And once you can spot them, you’re much less likely to make them yourself.
In this session, we will sharpen our mistake-detecting skills by looking at a collection of fake proofs: arguments that look convincing at first glance, but hide a sneaky error somewhere inside. Your job is to find where things go wrong and explain why.