Question

Exercise 2. prove the statement, Let a, x and y are real numbers so that x < y and a > 0. Then ax < ay

Answer 1

Here given that $a,x$ and $y$ are real number such that $x<y$ and $a>0.$

So by the given conditions we have $(y-x)>0$ and $a>0.$

Again we know that if $m,n\in R$ and $m>0,n>0$ then $m.n>0.$

As $x,y\in R$ then $(y-x)\in R$ .

So by the properties of real number

$a.(y-x)>0$

$\implies ay-ax>0$

$\implies ay>ax$

Which completes the proof.