Proof by deduction, exhaustion and counter-exampleEdexcel A-Level Maths: Mind map

Exam questions on Proof by deduction, exhaustion and counter-example

1. A student claims that $n^2+n+41$ is a prime number for every positive integer $n$.
   Show that the claim is false for $n=41$, and state what type of proof this is.2 marks
2. The function $f(n)=n^2-6n+10$ is defined for all real $n$.
   Hence prove that $n^2-6n+10$ is positive for all real $n$.2 marks
3. Two consecutive integers are $n$ and $n+1$, where $n$ is an integer.
   Prove that the sum of the squares of the two integers is always odd.3 marks