 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 are two sets such that x has 40 elements, x union y has 60 elements and x in the section y has 10 elements how many elements does y have? So first let us learn that if x and y are two finite sets such that they have some common elements then number of elements in x union y is equal to number of elements in the set x thus number of elements in the set y minus number of elements in the set x intersection y so with the help of this formula we will find the solution of the above problem so this is our idea let us now start with the solution and we are given that x has 40 elements the number of elements in the set x is equal to 40 and x union y has 60 elements the number of elements in the set x union y is equal to 60 and x intersection y has 10 elements so number of elements in the set x intersection y is equal to 10 Let us now write the formula that is n, 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 putting the values, number of elements in the set x union y is equal to 60 which is equal to number of elements in the set x that is 40 plus we have to find the number of elements in the set y, so number of elements in the set y minus the number of elements in the set x intersection y that is 10, thus you further ask 60 is equal to 40 minus 10 is 30 plus number of elements in the set y or you can further be written as number of elements in the set y is equal to 60 minus 30 which is equal to 30, thus the number of elements in the set y is equal to 30, so this completes the solution hope you enjoyed it take care and have a good day.