 Hi and welcome to the session. I am Asha and I am going to help you with the following question it says which of the following pairs of sets are disjoint? So first let us learn what are disjoint sets. The intersection of two sets is a null set then the two sets are said to be disjoint that is a and b are two disjoint sets if a intersection b is equal to a null set. The help of this definition will solve the above problem so this is the idea. With the solution first part says to check whether the pair 1, 2, 3, 4, x such that x is a natural number less than or equal to x is less than or equal to 6 are disjoint. So first let us name these two sets as a and b as the set having elements 1, 2, 3, 4 and b is the set having elements all those natural numbers which are less than or equal to 6 and greater than or equal to 4 so the elements are 4, 5 and 6. Now to check whether a and b are disjoint we will have to first find a intersection b and a intersection b will have all those elements which are common to both a and b and the common element here is 4. This implies that a intersection b is not a null set and hence a and b are not disjoint that is the given pair is not disjoint. So our answer is not disjoint it completes the first part and now proceeding on to the second part which is a is two sets as a and b and now it is find the intersection of a and b if it comes to be 5 then the two sets are disjoint otherwise not. So the common element is e how there is no other common element so the intersection of a and b is the set of all those elements which are common to both a and b and that is e. So this implies a intersection b is not equal to 5 and hence the two sets are not disjoint which completes the second part and now proceeding on to the last part two sets first is x such that x is an even integer the second set is x such that x is an odd integer. Now let us name the first set as a and the second one as b so a will comprise of all those elements which are even integers that is starting from minus infinity to minus 4 minus 2 0 2 4 and so on up to infinity so all these are even numbers and the set b will have elements minus infinity to all those elements which are not divisible by 2 which are minus 3 minus 1 1 3 and so on. So all these numbers are odd numbers and now we need to find a intersection b and on observing the two sets we find that there is no element which is common to both the sets and hence the intersection of a and b is 5 so this implies a and b are disjoint sets so these two sets are disjoint and thus our answer is to find which of the given pair is disjoint so the third pair is disjoint so this completes the solution hope you enjoyed it take care and have a good day.