 Hello and welcome to the session. In this session we will discuss the following question and the question says, from the given WEN diagram find the following first part is p, second part is q, third part is p union q and fourth part is p intersection q. Also verify that number of elements in p plus number of elements in q is equal to number of elements in p union q plus number of elements in p intersection q. We are given this WEN diagram where the set p is represented by the outer circle and the elements of p are inside this outer circle and the set q is contained in p and is represented by this inner circle and the elements of q are inside the inner circle. Let's start the solution now. The first part is we have to find what is p. Now the set p contains all the elements which are inside this outer circle. So we will change this area which represents the set p in yellow. So this shaded portion contains all the elements of the set p. Now this shaded portion contains the elements 0, 1, 3, 9, 2, 4, 6, 8. So p is equal to the set containing the elements 0, 1, 2, 3, 4, 6, 8, 9. So this is our answer for the first part. Now in the second part we have to find q. Now set q is represented by this inner circle. So the elements of q are all the elements which are inside this circle. So this shaded portion in yellow is the set q and it contains the elements 0, 1, 3 and 9. So q is equal to the set containing the elements 0, 1, 3, 9. This is our answer for the second part. Now in the third part we have to find p union q. Now p union q contains elements which are in p or in q or both. So this shaded portion represents the set p union q and it contains the elements 2, 4, 6, 8, 0, 1, 3, 9. So p union q is equal to the set containing the elements 0, 1, 2, 3, 4, 6, 8, 9. Now in the fourth part we have to find p intersection q. Now p intersection q contains all those elements which are common to both the sets p and q. That is all the elements which are there in the common portion between these two circles p and q. Now all the elements inside this inner circle are the elements of both p and q. So p intersection q is this shaded portion and it contains the elements 0, 1, 3, 9. So p intersection q is equal to the set containing the elements 0, 1, 3, 9. This is our answer for the fourth part. Now we have to verify that number of elements in p plus number of elements in q is equal to number of elements in p union q plus number of elements in p intersection q. Now in the first part we found the set p and we can see that set p contains 8 elements. So number of elements in p is equal to 8. Also from the second part we can see that the set q contains 4 elements. So number of elements in q is equal to 4. In part 3 we found the set p union q and we can see that p union q contains 8 elements. So number of elements in p union q is equal to 8 and using part 4 we can say that the number of elements in the set p intersection q is equal to 4. That is number of elements in p intersection q is equal to 4. Therefore number of elements in p plus number of elements in q is equal to 8 plus 4 which is equal to 12. Let this be equation number 1 and number of elements in p union q plus number of elements in p intersection q which is equal to 8 plus 4 which is same as 12. Let this be equation number 2. Now from equations 1 and 2 we get number of elements in p plus number of elements in q is equal to number of elements in p union q plus number of elements in p intersection q. Hence proved. With this we end our session. Hope you enjoyed the session.