 Hi and welcome to the session. Let us proceed on with the question which is given to us. It says in a survey of 60 people it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both T and I, 11 read both H and T, 8 read both T and I, 3 read all the 3 newspapers. Find for the first part the number of people who read at least one of the newspapers and the second part says the number of people who read exactly one newspaper. Right, so in this question we will use Wayne diagrams which will show us the relationship between the sets. Let this be the universal set. This be the set of people reading newspaper H, this set be the set of people reading newspaper T and this be the set of people reading newspaper H. Now we have denoted H with the set of people reading newspaper H, denoted T with the set of people reading newspaper T and I denoted the set of people reading newspaper H. Right, now to simplify we have drawn a Wayne diagram showing all the 3 sets intersecting each other. We denote the number of elements in specific region by letters A, B, C, D, E, F. Now let us have element A, B, D, C, E, F, G in all the 3 sets. Now it says that A plus B, now here A plus B plus C plus D will represent the number of people reading newspaper H. Similarly B plus C plus E plus F will represent the people reading the newspaper T, D, C, E, G are the elements in set I, then we have H intersection T which include the elements B and C, so that means B plus C should be equal to 11 that is given to us. C plus E represent T intersection I, H intersection I represent by elements C and D and all the 3 elements are intersected at a common point, common element C. So according to what information we are given, we are given that this universal set consists of 60 people out of which 25 people read newspaper H, 26 read T, 26 read I, 9 read both T and I, 11 read both T and H, 8 read both T and I and 3 read all the 3 newspapers. So we equate the elements like this by the given data we have number of people reading newspaper H as elements A plus B plus C plus D that is equal to 25 let it be represented by equation I, number of people reading newspaper T. So this is the information which is given to us in the question and we have represented the equation in the form of equations and equated with the numbers we have been given. Right, now we need to find the number of people who read at least one of these 3 newspapers that means we need to find the number of people where H union T union I basically. So we can find it out with the above region and using one of the formulas that is known to us that will be H union T union I will give us by adding first of all all the elements of all the 3 sets then subtracting their intersections that means H intersection T subtracting H intersection I subtracting T intersection I and then subtracting and then adding the number of elements that are common to all the 3 sets. So we just plug in the values that we have from above and on doing so we have H union T union I will give us 25 plus 26 plus 26 then we need to subtract so minus H intersection T that will be 11 minus 8 minus 9 plus 3 that is number of elements that are common to all the 3. So the answer comes out to be 52. So 52 is the answer of the first part that is number of people who read at least one of the 3 newspapers. So this completes the first part. Then in the second part we need to find number of people who read exactly one newspaper that is to find A plus F plus C. Now putting or substituting the value of C from the above equation that we had that is equation 7 in 4, 5 and 6 in this, this and this we can get the value of B, E and D right. So let us so on doing so we have the values as B plus C gives us 11 we know that the value of C is 3 so we get the value of B as equals to 8. So we have substituted the value of C from 7 in 4, 5 and 6. So we have the value of B similarly we will have the value of C because we E that is C plus C is equal to 8. So 3 plus E will be 8 the value of E will be 5 and lastly C plus D in equation 6 is given to us as 9, C is 3 from equation 7. So we have the value of D as 6 right. Now on substituting the value of D, C, E in the third equation we will have D plus C plus E plus C was 26. Now let us substitute the value of D is 6, C is 3, E is 5 and we have the value of G coming as 12. Now substituting the value of B, C and E in second equation we will get 8 plus 3 plus 5 plus F is equal to 26. So the value of F comes out to be 10. Now we left with finding out the value of A so on substituting the values in first we have 8 plus 3 plus 6 plus A is equal to 25 that gives us the value of A as 8 thus we get A plus G plus F as 8 plus 12 plus 10 that is 30. So number of people who read exactly one newspaper is equal to 30 and this is our required answer of the second part. So I hope you enjoyed the session and in the last part we found out the value of A, F and G because we wanted to find out the people who read exactly one newspaper and A belongs here, F belongs here having no intersection and no elements are repeated over here. So with the help of this Vane diagram we were able to first of all simplify our question using these elements and it made our perception more clear. So that was our key idea of the question that helped us in solving the required questions successfully. So in these type of questions try to make a Vane diagram and you will be able to find out your answer more easily and bye for now.