Question

Is the following example of null set: set of odd natural numbers divisible by 2.

Answer 1

Hint: We have to first define the term null set. We also find the set of odd natural numbers and find which of them is divisible by 2. We explain that there exists no odd natural number which is divisible by 2. We get the null set.

Complete step-by-step answer:
Set of odd natural numbers divisible by 2 is an example of a null set.
The null set defines the set which has no element in it.
There exists no odd natural number which is divisible by 2.
The set of odd natural numbers is $A=\{1,3,5,7,....\}$. None of them is divisible by 2.
So, if B is the set of odd natural numbers divisible by 2, then $B=\left\{\right\}=\varphi$ and $n\left(B\right)=0$.
So, the correct answer is “Option B”.

Note: In mathematical analysis, a null set is a set that has measure zero. This can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total length. The notion of a null set should not be confused with the empty set as defined in set theory.