Question

Show that subtraction are not binary operation on natural number N

Answer 1

$N\times N=N$

where $(a,b)=a-b$

here $a$ and $b$ are natural numbers (i.e. 1,2,3,.......)

let , $a=3$ and $b=5$

$a-b=3-5$

$=-2\notin N$

$\therefore$ substraction is not a binary operation on $N$