```Question 174659
Which of the following sets is closed under division?
a. nonzero whole numbers
<pre><font size = 4 color = "indigo"><b>
No, it's not closed because it's possible to divide our
way out of the set of whole numbers. For example we can
divide them and get 2.5, which is NOT a whole number.
So we have divided our way out of the set of whole
numbers.  Since this is possible, the set of
nonzero whole numbers is not closed under division.
</b></font></pre>
b. nonzero integers
<pre><font size = 4 color = "indigo"><b>
No, it's not closed, for non-zero whole numbers are
nonzero integers, and the above example shows that
it's not closed.
</b></font></pre>
c. nonzero even integers
<pre><font size = 4 color = "indigo"><b>
No because it's possible to divide our way out of the set of
even integers, say 8 and 6, and divide them and get {{{4/3}}}, which
is NOT a nonzero even integer. So we have divided our way out of the
set of nonzero even integers.  Since this is possible, the set of
nonzero even integers is not closed under division.
</b></font></pre>
d. nonzero rational numbers
<pre><font size = 4 color = "indigo"><b>
Yes because it is impossible to divide our way out of the set of