 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 a set containing elements 3, 5, 7, 9 and 11, B have elements 7, 9, 11 and 13, C have elements 11, 13 and 15 and D have elements 15 and 17, then we have to find the solution of following 10 parts. So before finding the solution, let us first learn that what is the intersection of any two sets. Suppose A and B are any two sets, then A intersection B will have all those X such that X belongs to A and B both. So the definition of intersection of two sets is the main idea with the help of which we will solve this problem. So it is the idea. Let us now start with the solution. First we have to find A intersection B. Now A have elements 3, 5, 7, 9 and 11 and B have elements 7, 9, 11 and 13. Now A intersection B will have all those elements which are both in A and B. Now 7 is in A also and in B also. 9 is also in A as well as in set B and 11 is also in set A as well as in set B. So A intersection B will have elements 7, 9 and 11. So the set which is the intersection of A and B will have elements 7, 9 and 11. So this completes the first part and now proceeding on to the next part. Here we have to find the intersection of sets B and C. Now B is set having elements 7, 9, 11 and 13 and C have elements 11, 13 and 15. So B intersection C will have elements which are both in B and C and the elements are 11 and 13. So B intersection C will have 11 and 13 as elements and so our answer is the intersection of two set is the set having elements 11 and 13. This completes the second part and now proceeding on to the third part where we have to find the intersection of A, C and D. Now A is a set having elements 3, 5, 7, 9 and 11, C is a set having elements 11, 13 and 15 and D is a set having elements 15 and 17. So the intersection of all these three sets will have elements which are in all three of them. On observing we find that there is no element which is common to all these three sets. Hence the set which is the intersection of all these three sets is an empty set and so our answer is 5. That is an empty set. This completes the third part and now proceeding on to the fourth part where we have to find A intersection C. Now A is a set having elements 3, 5, 7, 9 and 11 and C is a set having elements 11, 13 and 15. Now we have to find an element which is common to both these sets and there is only one element 11 which is in both the sets A and C. So A intersection C is a single set having only one element and that element is 11. Here's our answer is the intersection of set A and C is a set having only one element that is 11 and this completes the fourth part. Now proceeding on to the fifth part where we have to find B intersection D. Now B is a set having elements 7, 9, 11 and 13 and D is a set having elements 15 and 17. We have to find B intersection D. This set will have elements which are common to both B and D. And on observing we find that there are no elements which are common to both set B and D, therefore B intersection D is 5. Hence B intersection D is a set having no elements that is an empty set. So this completes the fifth part. Now proceeding on to the sixth part where we have to find A intersection B union C. Now A is a set having elements 3, 5, 7, 9, 11, B is a set having elements 7, 9, 11 and 13 and C is a set having elements 11, 13 and 15. So first we will find what is B union C. Now B union C will have all the elements which are either in B or in C or in both. So the elements which are either in B or in C or in both are 7, 9, 11, 13 and 15. And now we have to find A intersection B union C. That is we have to find the intersection of set A and let us name the set B union C as E. We are required to find the intersection of A and E. Now the intersection of A and E will be the elements which are both in the set A and E. And on observing we find that 7 is in both the sets, 9 is in both the sets and 11 is also an element which is common to both A and E. So the intersection of A and the set E will have elements 7, 9 and 11. Our answer is the set having elements 7, 9 and 11. This completes the next part and now proceeding on to the seventh part where we have to find A intersection T. Now A is the set having elements 3, 5, 7, 9 and 11 and D is the set having elements 15 and 17. Now A intersection D will have all those elements which are both in A and D. And on observing we find that there are no elements which are common to both A and D. Therefore A intersection D is an empty set. Hence our answer is the intersection of sets A and D is an empty set. So this completes the seventh part and now proceeding on to the eighth part where we have to find A intersection B union D. So A is the set having elements 3, 5, 7, 9 and 11, B is the set having elements 7, 9, 11 and 13 and D is the set having elements 15 and 17. So first of all let us find out B union D. So B union D will have all those elements which are either in B or in D or in both. So these elements are 7, 9, 11, 13, 15 and 17. Let us name this set as F. According to the question we have to find out the intersection of A and the union of B and D. This can also be written as A intersection F. Now A intersection F will have all those elements which are common to both the sets A and F. So the first common element is 7, 9 is also a common element, 11 is also a common element. So the intersection of A and F will have elements 7, 9 and 11. That is the intersection of A and the union of B and D is a set having elements 7, 9 and 11. So this completes the eighth part and now proceeding on to the ninth part where we have to find A intersection B, intersection B union C. Now A is a set having elements 3, 5, 7, 9 and 11, B is a set having elements 7, 9, 11 and 13 and C is a set having elements 11, 13 and 15. So to find this first we will find A intersection B then we will find B union C and then we will find the intersection. So first let us find A intersection B. A intersection B will have all those elements which are both A and B. So the elements which are common to both A and B are 7, 9, 11. Let us name this set as X and now let us find B union C which will have all those elements which are either in B or in C or in both. So the elements which are either in B or in C or in both are 7, 9, 11, 13 and 15. Let us name this set as set Y. Now into the question we have to find out A intersection B, intersection B union C and A intersection B is nothing but X. Intersection B union C is a set Y and now we will find the intersection of X and Y that is the common elements in X and Y are 7, 9 and 11. So the intersection will have elements 7, 9 and 11. Thus A intersection B, intersection B union C will be a set having elements 7, 9 and 11. So that completes the ninth part. Now proceeding on to the tenth part where we have to find intersection B union C. Now A is a set having elements 3, 5, 7, 9 and 11. B is a set having elements 7, 9, 11 and 13. C is a set having elements 11, 13 and 15. And D is a set having elements 15 and 17. So to find this first we will find A union D. A union D will have all those elements which are either in A or in D or in both. So the elements are 3, 5, 7, 9, 11, 15 and 17. Let us name this set as X and now we will find B union C and B union C will have all those elements which are either in B or in C or in both. So the elements are 7, 9, 11, 13 and 15. And let us name this set as Y. Now we have to find A union D intersection B union C. That is we have to find X intersection Y. Now X intersection Y will have all those elements which are common to both X and Y and the elements are 7, 9, 11 and 15. Thus our answer is the set having elements 7, 9, 11 and 15. So this completes the solution. Hope you enjoyed it. Take care and bye for now.