 Hi and welcome to the session, I am Asha and I am going to help you with the following question which says if A is equal to 1, 2, 3, 4, B is equal to the states containing elements 3, 4, 5, 6, C contains elements 5, 6, 7, 8 and D is equal to the states containing the elements 7, 8, 9, 10, we have to find the union of these 6. So first let us learn that if we have any 2 states A and B then the union is equal to all those elements x which are either in A or in B or in both. So this is the key idea we are going to use in this problem to find the union of these 6. Now start with the solution first we have to find A union B. Now A is the state containing elements 1, 2, 3 and 4 and B is the state containing elements 3, 4, 5 and 6. So A union B will contains all the elements which are either in A or in B or in both. So first we have 1, 2, 3 is in both the states and 4 is also in both the states and then 5 and 6. That is the union of A and B is 1, 2, 3, 4, 5 and 6. So this completes the first part and now proceeding into the second part where we have to find A union C. Now A is the state which has elements 1, 2, 3 and 4 and C is the state which has elements 5, 6, 7 and 8. And union of A and C will have all those elements which are either in A or in C or in both. So these elements are 1, 2, 3, 4, 5, 6, 7 and 8. That is our answer is 1, 2, 3, 4, 5, 6, 7 and 8. So this completes the second part and now proceeding on to the third part where we have to find B union C. Now B is the state having elements 3, 4, 5 and 6 and C has elements 5, 6, 7 and 8. Thus B union C will have all the elements which are either in B or in C or in both. So these elements are 3, 4, 5 and 6 are both in the state B also and C also. So we have 5, 6 in the union and 7 and 8. Thus our answer is 3, 4, 5, 6, 7 and 8. This completes the third part and now proceeding on to the fourth part where we have to find the union of states B and D. Now state B is 3, 4, 5 and 6 and the state D have elements 7, 8, 9 and 10. So B union D will have all the elements which are either in B or in B or in both. So these elements are 3, 4, 5, 6, 7, 8, 9 and 10. And thus our answer is 3, 4, 5, 6, 7, 8, 9 and 10. This completes the fourth part and now proceeding on to the fifth part where we have to find the union of states A, B and C. Now here the state A has elements 1, 2, 3 and 4. The state B has elements 3, 4, 5, 6 and the state C has elements 5, 6, 7 and 8. So the union of A, B and C will have all those elements which are either in A or in B or in C or in all three of them or in any two of them. So these elements are 1, 2, 3 and 4 are both in the state A and B and we have 5 and 6 which are also both in state B and C. And lastly we have 7 and 8 as the union of A, B and C contains elements 1, 2, 3, 4, 5, 6, 7 and 8. So this completes the fifth part and now proceeding on to the sixth part where we have to find the union of A, B and D. Now A is the state which have elements 1, 2, 3 and 4 state B have elements 3, 4, 5 and 6 and the state D has elements 7, 8, 9 and 10. Now the union of all these three sets will have elements which are either in A, B or C or in all three of them or in any two of them. So these elements are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. So the union have elements 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. So this completes the sixth part. Now proceeding on to the last part where we have to find the union of B, C and D. Now we have elements 3, 4, 5, 6, set C have elements 5, 6, 7 and 8, set D have elements 7, 8, 9 and 10. The union of these three sets will have all the elements which are either in B, C or D or in all three of them or in any two of them. So these elements are 3, 4, 5, 6, 7, 8, 9 and 10. Hence the union of elements 3, 4, 5, 6, 7, 8, 9 and 10. So this completes the last part. This completes the solution. Hope you enjoyed this session. Take care and have a good day.