 Hello and welcome to the session. In this session we will discuss brain diagrams showing relationship between given sets. Now let us discuss difference of sets using brain diagrams. Now difference of two sets and B is given by A-B is a set containing the element X such that X belongs to A but X does not belongs to B. Now B can be subset as the case when A and B are overlapping sets. Now we will look by using brain diagrams when A and B are overlapping sets. Now this is the rectangle representing the universal set U. Now these two circles are representing the two sets A and B which are over B is the region so the shaded region is in A but not in B which is representing A-B when A and B are overlapping sets. Let us draw a brain diagram representing B-A. Now this is the brain diagram which is representing and B and this rectangle is representing the universal set. That means A and B are the subsets of the universal set. Now here we have to represent B-B by this brain diagram. That means we have to shade that region of B which is not in A. Now this region represents B-A that means this region which is shaded is in B but not in A. Now let us discuss the case when A and B are disjoint sets. The brain diagram representing A-B when A and B are disjoint sets. Now this is the brain diagram representing two and B which are disjoint sets. Now here A-B that means those elements of A which are not in B. So in this case we will shade that region of A which is not in B. This region is representing A-B that is the elements of A which are not in B. So this is the representation of A-B by using the brain diagram. A and B are disjoint sets. The brain diagram representing B-A are to disjoint find B-A. That means those elements of B which are not in A. So we will shade that region of B which is not in A. This region which is representing B-A that is region of B which is not in A. So this is the brain diagram representing B-A whenever A and B are disjoint sets. Next case when A is a proper subset of the brain diagram representing A-B when A is a proper subset of B. The diagram representing that means all elements of A are contained in B. We have to find the bad region of A which is not in B. But here there is no region of A which is not in B. So here nothing will be shaded. So this is the brain diagram representing A-B when A is a proper subset of B. Now let us draw a brain diagram representing B-A in this case. Now here we have to shade that region of B which is not in A. Now this larger circle is representing the set B and the smaller circle is representing the set A. Now this shaded region represents C-B which is not in A. So this is the representation of B-A when A is a proper subset of B. The representation of C-B whole complement and A intersection B whole complement. This when A and B are overlapping sets. Now in the first part we have to represent A and B whole complement when A and B are overlapping sets. Now I am representing A and B which are overlapping sets. Now here we have to find A and B whole complement. That means those elements which are not in A union B. So we will shade that region which is not in A union B. That is all the portion inside the rectangle excluding these two circles. As these two circles that is these two overlapping circles are representing A union B. As representing A union B whole complement. To make V and I a representing A intersection B whole complement. Now in case of overlapping sets this overlapping portion is representing A intersection B whole complement. That means that region which is not in A intersection B. But in the universal set at the shaded region is representing A intersection B when A and B are when A and B are in diagram representing whole complement when A and B are disjoint sets. Now here we have to name the main diagram to represent A and B and B whole complement. Now this is the main diagram representing A and B are disjoint sets. Now we will shade that region which is not in A union B. We will shade inside the rectangle excluding the region that is this circle which is representing the set A and this circle which is representing the set B. Now here this shaded region is representing A union B whole complement. Whole complement when A and B are disjoint sets. Similarly let us try a main diagram representing A intersection B whole complement when A and B are disjoint sets. Now for this we have to which is not in A intersection B and B are to disjoint sets. That means there is no region for the intersection of these sets. The whole of the universal set will represent A intersection B whole complement when A and B are disjoint sets. This rectangle is shaded that is the universal set is representing B whole complement when A and B are disjoint sets. Now let us discuss the case when A is a proper subset of B. Now let us draw a main diagram representing complement when A is a proper subset of B. Now as A is a proper subset of B that means all values of A are contained in B and U and B will be this larger circle which is representing the set B. They will share all this portion inside this rectangle excluding the portion or the region which is representing A union B that means the set B which is the larger circle. The shaded portion or the shaded region is representing A union B whole complement when A is a proper subset of B. Now let us draw a main diagram representing A intersection B whole complement. Now for A intersection B whole complement we will shade that region which is larger than A intersection B. And here A intersection B is represented by the smaller circle which is representing the set A. That means we will shade inside this rectangle excluding this portion which is representing A intersection B whole complement. Now let us discuss B union C and A intersection B intersection C. Now let us discuss when A, B and C are three overlapping sets. In diagram representing A union B union C when A, B and C are three overlapping sets. Now this is the main diagram representing three overlapping sets. Now here we have to find A union B union C. Now here these three circles together will represent A union B union C. So we will shade all this region that is the circle A, B and C. Therefore the shaded region is representing A union main diagram representing A intersection B intersection C. Now we have to represent A intersection B intersection C. For the three overlapping sets. Now for the intersection we will shade the region which is common to all the three circles. Now this region is common to all the three circles. So therefore the shaded region is representing A intersection B intersection C. Now let us discuss when representing A union B union C when A, B and C are three disjoint sets. Now here A, B and C are three disjoint sets. Now as A, B and C are disjoint sets. So here these three circles together will represent that means we have to shade the circle A the circle B. and the circle C. Now the shaded region is representing A union B union C. Then A, B and C are three disjoint sets. Now let us draw the main diagram representing A intersection B intersection C in this case. Now A, B and C are three disjoint sets. Now we have to represent A intersection B intersection C. That means we have to represent the common region to these three sets. But here as A, B and C are three disjoint sets. So there is no portion or no region in common to these three circles. That means there is nothing to be shaded in this case. So this is the representation of A intersection B intersection C when A, B and C are three disjoint sets. So in this session you have learnt about main diagrams showing relationship between given sets. And this concludes our session. Hope you all have enjoyed the session.