 Hello and welcome to the session. In this session we will discuss the following question and the question says, in a class of 50 students, 20 study French language, 15 study German, 7 study both German and French, draw a Venn Diagram to find the number of students who study first either French or German, second neither French nor German. Let's start the solution now. Let S be all students of the class. F is equal to students who study French language. G is equal to students who study German language. So we have denoted all students of the class by the set S, students who study French language are denoted by the set F and students who study German language are denoted by set G. Now in the first part we have to draw a Venn Diagram and find the number of students who study either French or German. We shall first draw the Venn Diagram which represents the sets S, F and G. First we draw a rectangle which represents the universal set S. Next we draw two intersecting circles which represent the sets F and G. Since F and G are overlapping sets, so we have represented them by intersecting circles. We are given in the question that the total number of students who study French language is 20 and 7 students study both German and French. So we write 7 in this common portion between the two circles F and G. Now the total number of students in F are 20 and in the common region between F and G there are 7 students. So the number of students in the remaining region of F are 20 minus 7 which is equal to 13. So we write 13 in this remaining portion of the circle F. Now it is given in the question that the total number of students who study German language are 15. So the total number of students in the set G is 15 and the number of students in the common region between the sets F and G are 7. So the number of students in the remaining region of the set G are 15 minus 7 which is equal to 8. So we write 8 in this remaining portion of the circle G. We now shade the region which represents the number of students who study either French or German. So this shaded portion represents the number of students who study either French or German. So we can say that number of students who study either French or German are 13 plus 7 plus 8 which is equal to 28. So this is our answer for the first part. Now in the second part we have to draw a Venn diagram and find the number of students who study neither French nor German. As done in the first part, we draw a Venn diagram for the sets F, G and S where S which is the universal set is represented by the rectangle and the sets F and G are represented by intersecting circles. Now we have to find the number of students who study neither French nor German. That is we have to find the number of students who are in the set S but not in the sets F or G. So we have to find the number of students who are in this remaining region of the set S outside these circles. We are given in the question that the total number of students in the class are 50. So we can say that number of students who study neither French nor German are total number of students which is 50 minus the number of students which are in F or in G which is equal to 13 plus 7 plus 8 which is equal to 22. So we write 22 in this rectangle S outside the circles F and G. So the shaded portion represents the number of students who study neither French nor German. With this we end our session. Hope you enjoyed the session.