 Hi and welcome to the session. I am Asha and I am going to help you with the following question that says in a group of 70 peoples that is 7 like coffee, 52 like tea and each person like at least one of the 2 drinks how many people like both coffee and tea? So first let us learn a simple formula that says if C and T are 2 finite sets then number of elements in C union T is equal to number of elements in the set C plus number of elements in the set T minus number of elements in the set C intersection T so this is the key idea we are going to use in this problem to find that how many people like both tea and coffee Let us now start with the solution and let set of people who like coffee be denoted by C the set of people who like tea be denoted by T then C intersection T will be the set of people who like both tea and coffee So by the key idea we have number of people who like tea or coffee is equal to number of people who like coffee plus number of people who like tea minus number of people who like both coffee or tea putting the values now we are given that number of persons who like coffee 37 number of persons who like tea are 52 and the total number of persons that is N C union T is equal to 70 so substituting the values we have 70 is equal to 37 plus 52 minus number of persons who like both tea and coffee so we have 70 is equal to 89 minus number of people who like both coffee and tea and further implies that number of persons who like coffee and tea is equal to 89 minus 70 which is further equal to 19 plus number of people who like coffee and tea is equal to 19 So this completes the solution hope you enjoyed it take care and bye for now