Question

Show that every positive integer is either even or odd..

Answer 1

Let $I$ be a positive integer

We can now write $I$ in the from of

$I=pq+r$

So, $pq+r$ can either be even or odd.

Since, $pq+r$ yields either even or odd number

$\Rightarrow$ if $pq+r$ is even

$pq+r=2x$

and if odd

$pq+r=2x+1$

So, $I=2x$ or $2x+1$

$\Rightarrow I=$odd or even