Problems on set-VII

               In this page 'Problems on set-VII' we are going to see problems on Venn diagrams and problems based on some rules.

                Parents and teachers can guide the students to do the problems on their own. If they are having any doubt they can verify the solutions.

 1.          In an examination 150 students secured first class in English or Maths. Out of these 50 students obtained first class in both English and Maths.  115 students secured first class in Maths.  How many students secured first class in English only?

2.           In a group of 30 persons, 10 take tea but not coffee. 18 take tea. Find how many take coffee but not tea, if each person takes at least one of the drinks?

3.           In a village there are 60 families.  Out of these 28 families speak only one language and 20 families speak other language. How many families speak both the languages?

4.           In a school 150 students passed X standard Examination. 95 students applied for group I and 82 students applied for group II for the further studies. If 20 students applied neither of two, how many students applied for both groups?


5.           Sam is a section chief for an electric utility company. The employees in his section cut down tall trees or climb poles. Sam recently reported the following information to the management of the utility.

             Out of 100 employees in my section, 55 can cut tall trees, 50 can climb poles, 11 can do both, 6 can't do any of the two. Is this information correct?

6.          A and B are two sets such that n(A-B) = 32 +x, n(B-A) = 5x and  n(A∩B) = x.  Illustrate the information by means of a Venn diagram. Given that n(A) = n(B). Calculate (i)the value of x  (ii) n(A∪B).

7.            The following table shows the percentage of the students of a school who participated in Elocution and Drawing competitions.

              Draw a Venn diagram to represent this information and use it to find the percentage of the students who

       (i)  participated in Elocution only

       (ii) Participated in  Drawing only

       (iii) Do not participate in any one of the competitions.

8.           A village has total population 2500. Out of which 1300 use brand A soap and 1050 use brand B soap and 250 use both brands. Find the percentage of population who use neither of these soaps.




Students can try to solve the problems in this page 'Problems on set-VII' on their own. Parents and teachers can encourage the students to do so. They can verify their answers with solutions given in this page. If you are having any doubt you can contact us through mail, we will help you to clear your doubt.

                                      Set Theory