Structure of proof and proof by exhaustionEdexcel International A Level Maths: Mind map

Exam questions on Structure of proof and proof by exhaustion

1. A statement S is made: for every integer $n$ with $1\le n\le5$, the value of $n^2+n$ is even.
   Prove that S is true by exhaustion.2 marks
2. $x$ and $y$ are odd positive integers, each less than 7.
   Prove that $x+y$ is divisible by $2$ for every possible pair.2 marks
3. Let $f(n)=n^3-n$, where $n$ is an integer.
   Use proof by exhaustion to show that $f(n)$ is divisible by $6$ for every integer $n$ with $2\le n\le6$.3 marks