Question

the collection of all non zero rational numbers is closed under division​

Answer 1

Answer with explanation:

  $Q=\frac{x}{y},\text{y}\neq 0.,x\epsilon I(\text{Integer}),y\epsilon I(\text{Integer}),\\\\{\frac{x}{y}}\neq 0$

To Check : Whether collection of all non zero rational numbers is closed under division​

Proof:

  Let ,x=2

y=3

$\Rightarrow\frac{x}{y}=\frac{2}{3}=Q\epsilon (\text{Rational number})$

General rule

If, a and b are any two non zero rational numbers,that is $\frac{a}{1}, \frac{b}{1}$ are rational number, then $\frac{a}{b}$ ,will be also a Rational number.

Hence , collection of all non zero rational numbers is closed under division​.