 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket and how many like tennis? Let us now learn that if C and T are any two finite sets such that they have some common elements then number of elements in T union C is equal to number of elements in the set C plus number of elements in the set T minus C. So with the help of this formula we will find the solution of the above problem. So this is the idea. Let us now start with the solution set of people who like cricket be denoted by C. The number of people who like cricket is equal to 40 as it is given to us 40 people like cricket and let set of people who like tennis be denoted by T and we have to find N of T number of people who like both cricket and tennis will be denoted by C intersection T and since the total number of people are 65 this implies number of C union T is equal to 65. Now let us write the formula which is actually idea that is number of elements and C union T is equal to number of elements in the set C plus number of elements in the set T minus C which implies the number of people who like cricket or tennis is equal to the number of people who like cricket plus the number of people who like tennis but not cricket. Now putting these values N of C union T is equal to 65 which is further equal to number of people who like cricket is equal to 40 plus number of people who like tennis but not cricket which implies that number of T minus C is equal to 65 minus 40 which is equal to 25. So N of T minus C is equal to 25. Now we will find the number of people who like tennis which we have denoted by N of T. This is what we have to find out and the formula to find the number of people who like tennis is N of T union C is equal to number of people who like tennis plus number of people who like cricket minus the number of people who like go tennis and cricket. Now number of people who like tennis or cricket is 65 which is equal to number of people who like tennis plus 40 minus 10 which is equal to 65 is equal to number of people who like tennis plus 30 which further implies that number of people who like tennis is 65 minus 30 which is equal to 35 and thus number of people only tennis and not cricket is equal to 25 number of people who like only tennis is equal to 35. So this completes the solution hope you enjoyed it take care and have a good day.