 Hi and welcome to the session. I am Asha and I am going to help you with the following question that says, if x and y are two sets such that number of elements in the set x is 17, number of elements in the set y is 23 and number of elements in the set x union y is equal to 38, find number of elements in x intersection y. So, first let us learn that if we have two finite sets suppose x and y and 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 the number of elements in x intersection y. So, this is our key idea we are going to use in this problem to solve it. Let us now start with the solution and we are given that number of elements in the set x is equal to 17, number of elements in the set y is equal to 23 and number of elements in the set x union y is equal to 38 and we are required to find the number of elements in the set x intersection y. So, first let us write the formula, formula is number of elements in x union y is equal to number of elements in x plus number of elements in the set y minus number of elements in the set x intersection y. Now, on substituting the values, number of elements in x union y is 38 is equal to number of elements in set x minus 17 plus number of elements in the set y that is 23 minus number of elements in the set x intersection y which further implies 38 is equal to on adding 17 by 23 we get 40 minus n x intersection y or taking number of elements in the set x intersection y on the left-hand side we are on the right-hand side we have 40 taking 38 on the right-hand side we have minus 38. So, we have number of elements in the set x intersection y equal to 2 that is our answer So, in this question we use the concept that number of elements of finite 6. So, this completes the solution hope you enjoyed it take care and have a good day.