Question

State whether the set given below is empty or not:
Set of odd natural numbers divisible by 2.

Answer 1

Hint: First we will find the elements in the set according to the given condition and then check if that thing is possible or not. Thus, we will have our answer. Odd numbers only end with 1, 3, 5, 7 or 9.

Complete step-by-step answer:
We will first see what is a set.
A set is a well defined collection of objects. The term “Well defined” refers to the fact that we cannot say that we have a set of intelligent students of Class 10 because the term intelligent varies according to every person. So, a set of intelligent students of Class 10 cannot be defined but however, if we take a set of students who scored marks greater than 90 is a well defined set.
We will now see what Natural numbers are.
Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity and are also used for counting purposes. It does not include zero (0). In fact, 1,2,3,4,5,6,7,8,9…., are also called counting numbers. Natural numbers are part of real numbers, that include only the positive integers i.e. 1, 2, 3, 4,5,6, ………. excluding zero, fractions, decimals and negative numbers.
So, Natural numbers ={1,2,3,4,5,.........}
Now we know that odd number is that number which is not divisible by 2.
So, Odd natural numbers ={1,3,5,.........}
We also know that odd numbers are not divisible by 2.
Hence, the set of odd natural numbers divisible by 2 is empty.

Note: We must be cautious of all the facts and definitions used in the solution.
We must read the question carefully because if the question was:-
State whether the set given below is empty or not:
Set of odd natural numbers which are not divisible by 2.
Then, the set of all the odd natural numbers would have been the answer which is definitely not empty.