 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says if x and y have two sets such that x union y has 18 elements, x has 8 elements and y has 15 elements, how many elements does x in the section y have? So first let us learn that if we have two finite sets x and y such that they have some common elements, then number of elements in x union y is equal to number of elements in x plus number of elements in y minus number of elements in x intersection y. So with the help of this formula we will find how many elements does x in the section y have? So this is a key idea that we will be using in this problem to solve it. Now start with the solution and we are given that x union y has 18 elements that is the number of elements in x union y is equal to 18. So x has 8 elements that is number of elements in the set x is equal to 8 and y has 15 elements so number of elements in the set y is equal to 15. Now let us write down the formula that is number of elements in x union y is equal to number of elements in the set x plus number of elements in the set y minus number of elements in the set x intersection y. Now let us replace then madam values number of elements in x union y is 18 and number of elements in the set x is 8 plus number of elements in the set y is 15 minus number of elements in the set x intersection y which implies that number of elements in the set x intersection y is equal to 23 which is the sum of 8 and 15 minus 18 which is further equal to 5. Thus the number of elements in the set x intersection y is equal to 5 and the answer is 5 which completes the solution hope you enjoyed it take care.