 Hello and welcome to the session. In this session we would discuss the following question which says identify the disjoint and the overlapping sets. In the first part we have a set A equal to set of digits in the number 2568 and set B is the set of digits in the number 3147. In the B part we have set C is equal to X such that X is equal to 5P where P belongs to W and P is greater than equal to 0 and less than 3. Set D is equal to Y such that Y is equal to 3Q where Q belongs to W and Q is greater than equal to 0 and less than 3. First of all we will define the overlapping sets and the disjoint sets. First we have the overlapping sets. Two sets are called overlapping sets if they have at least one element in common. Next we define the disjoint sets if two sets have no element in common they are called disjoint sets. This is the key idea that we would use in this question. Let's proceed with the solution now. In the first part of the question we have a set A which is the set of digits in the number 2568. So we can say that set A is equal to the set containing the elements 256 and 8. Then we have a set B which is the set of digits in the number 3147. So the set B could be written as the set containing the elements 3147. Now to check if these two sets are overlapping sets or disjoint sets we have to check if they have any common element or not. Now since in these two sets no element is common then according to the definition of the disjoint sets given in the key idea we find that the sets A and B are the disjoint sets. Now let's consider the next part in which we have a set C which is equal to x such that x is equal to 5p where p belongs to w that is the set of whole numbers and p is greater than equal to 0 and less than 3. So first of all let's find out the elements of the set C. Now since p belongs to w and also p is greater than equal to 0 and less than 3. So therefore p would take the values 0, 1 and 2. We also have x is equal to 5p. So putting the values of p as 0, 1 and 2 that is for p equal to 0, 1, 2 we obtain x equal to 0, 5 and 10. Thus we can say set C is equal to 0, 5 and 10. Now we have set T is equal to y such that y is equal to 3q where this q belongs to w that is the set of whole numbers and q is greater than equal to 0 and less than 3. Now we will find out the elements of the set D. Now q belongs to w that is the set of whole numbers and also q is greater than equal to 0 and less than 3. Therefore we get the values of q as 0, 1 and 2. We are given that y is equal to 3q. Now for q equal to 0, 1 and 2 we obtain y as 0, 3 and 6. Thus we can say the set D is equal to the set containing the elements 0, 3 and 6. Thus now we have got two sets set C containing the elements 0, 5 and 10 and the set D containing the elements 0, 3 and 6. We have to check if these two sets are disjoint sets or overlapping sets. For this we have to check if they have any element in common or not. So as you can see in these two sets C and D the element 0 is common that is 0 is common in both sets C and D. So according to the definition of the overlapping sets which says that two sets are overlapping sets if they have at least one element in common we find that the sets C and D are the overlapping sets. Thus we find the sets A and B are the disjoint sets and the sets C and D are the overlapping sets. So this completes the session hope you have understood the solution of this question.