Disproof by counter exampleEdexcel International A Level Maths: Mind map

Exam questions on Disproof by counter example

1. A statement T is made: for all real numbers $x$, $x^2>x$.
   Find a value of $x$ with $0<x<1$ and use it to show that T is false.2 marks
2. A student states: 'If $p$ is a prime number, then $p+2$ is also a prime number.'
   Find a counterexample to the statement with $p>10$. Show your working.2 marks
3. Consider the statement U: $n^2-n+1$ is a prime number for all integers $n\ge2$.
   Disprove U.3 marks