 Hello and welcome to the session. In this session, we discussed the following question which says from the given Venn diagram, that is this Venn diagram, list the following sets a complement, b complement, a union b complement and a intersection b complement. Before we move on to the solution, let's discuss the key idea to be used for this question. First of all, we have a complement. This is the set containing the element x such that x belongs to the universal set xi, but x does not belong to the set a. That is, it contains all the elements that belong to the universal set, but not the set a. Then, b complement would be the set containing the element x such that x belongs to the universal set xi and x does not belong to the set b. Now, a union b complement would be the set containing the element x such that x belongs to the universal set xi, but x does not belong to a union b. In the same way, we have a intersection b complement. This would be the set containing the element x such that x belongs to the universal set xi, but x does not belong to a intersection b. So, this is our key idea. Let's move on to the solution now. This is the Venn diagram given to us. From here, let's find out a complement. We know that a complement is the set containing the elements that belong to the universal set xi, but does not belong to the set a. Now, as you can see from this Venn diagram, only the element 6 and 7 do not belong to the set a, but are present in the universal set xi. So, we say that a complement is the set containing the elements 6 and 7. Then next, let's find out b complement. This is the set containing the elements which belong to the universal set xi, but does not belong to the set b. Now, in the set b, we have the elements 1 and 2. Rest of the elements are present in the universal set. So, we would say that b complement is the set containing the elements 3, 4, 5, 6 and 7. Then we have a union b complement. Now, this set would contain the elements in the universal set xi, but not in the set a union b. For this, first of all, let us find out the elements that belong to the set a union b. a union b would contain the elements that belong to both the sets a and b. So, as you can see from this figure, we have the elements 1, 2, 3, 4 and 5. These elements both the sets a and b. Now, a union b complement would contain the elements that do not belong to the set a union b, but are present in the universal set xi. Now, as you can see from the figure, only 6 and 7 are the elements that belong to the universal set xi, but are not present in the set a union b. So, we have a union b complement is the set containing the elements 6 and 7. Then next, we are supposed to find out a intersection b complement. This would contain the elements present in the universal set xi, but not in the set a intersection b. So, for this, first of all, let us find out the elements that belong to the set a intersection b. The elements that belong to the set a intersection b would be those elements that are common to both the sets a and b. Now, this set b is a subset of a set a. So, the elements present in set b would be common or you can say would be present in set a also. Thus, a intersection b is the set containing the elements 1 and 2. So, now, a intersection b complement would contain the elements that belong to the universal set xi, but are not present in this set. So, this would contain the elements 3, 4, 5, 6 and 7. So, thus we have got the answers for a complement, b complement, a union b complement and a intersection b complement. This completes the session. Hope you have understood the solution of this question.