 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says which of the following are example of null sets? First is set of odd natural numbers divisible by 2. Second is set of even prime numbers. Third is X such that X is a natural number where X is less than 5 and X is greater than 7. And the fourth one is Y such that Y is a point common to any two parallel lines. So first let us learn what are null sets which are also called empty sets or void sets which does not contain any element or a null set. So with the help of this idea we will solve the above problems so this is a key idea. I will put the first one which says of odd natural numbers divisible by 2. Numbers are the numbers which are non divisible by 2 that is 3 is odd number, 5 is odd number, 7, 9. All these numbers are odd numbers so there is no natural number which is divisible by 2 Hence the given set is null set. So our answer is a null set that is set of odd natural numbers divisible by 2 is a null set. That is there is no natural number, an odd natural number which is divisible by 2. So this completes this part and now proceeding on to the second part which says set of even prime numbers. Now even numbers are the numbers which are divisible by 2 that is 2, 4, 6, 8 and so on. And prime numbers are those numbers which have only two factors the number itself and 1. We have to find the set of even prime numbers so these are even numbers and only two is the number in this set which is prime since it is only two factors two itself and one. So even prime number this implies that this set contains one element the even prime number. Hence the given set is not a null set, not a null set. Now proceeding on to the third part which is X such that X is a natural number X less than 5 and X greater than 7. Now in this part the given set is the set of all X such that X is a natural number where X is less than 5 and also X is greater than 7. Now if a number is less than 5 then it can never be greater than 7 at the same time. So let us see numbers which are less than 5 are 4, 3, 2, 1, 0, minus 1 and so on. And numbers which are greater than 7 are 8, 9, 10, 11, 12. So observing these two we find that there is no number which is less than 5 and greater than 7. Hence we can say that the given set is a null set, null set which completes the third part and now proceeding on to the last part which says Y such that Y is a point common to any two parallel lines. The lines which never intersect or touch each other so in this case of parallel lines there is no point of intersection and therefore there is no such common point. So this set also has no elements. First let us write down parallel lines are the lines which never intersect. There is no point in common and so this set has no elements hence the given set is a null set and so our answer is a null set which completes the last part and on solving the above problem we found that 1, 3, 4 are null sets. In this question we understood the concept of null set and identified the given sets as null set or not a null set. So I hope you enjoyed this session. Take care and have a good day.