Question

Which of the following sets is closed under division?

natural numbers
non-zero integers
irrational numbers
non-zero rational numbers

Answer 1

non-zero rational numbers

Explanation:

Set is closed under division means:

For any two elements a and b in that set a/b must also belong to that set

Natural numbers :

1,2 are in the set of natural numbers but 1/2=0.5 is not in the set of natural numbers

Hence, set of natural numbers is not closed under division

Non-zero integers :

1,2 belongs to the set of non-zero integers but 1/2=0.5 is not in the set of non-zero integers

Hence, set of non-zero integers is not closed under division

Irrational numbers:

√2,√2 belongs to the set of irrational numbers but √2/√2=1 is not in the set of irrational numbers

Hence, set of irrational numbers is not closed under division

Non-zero rational numbers:

if p and q are any two non-zero rational then p/q is also a non-zero rational.

Hence, set of non-zero rationals is closed under division

Answer 2

The correct option is NON ZERO RATIONAL NUMBERS.
A rational number is a number that can be expressed as a fraction of two integers. A non zero rational number is a rational number that does not equal to zero. A set of number is said to be closed under division if all the problems that concern the set of numbers can be solved under division.