## Problems on set-VI

In this page 'Problems on set-VI' 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.  Place the elements of the following sets in the proper location on the given Venn diagram. U  =  {5,6,7,8,9,10,11,12,13}

M  =  {5,8,10,11}

N  =   {5,6,7,9,10}.

Some Important rules

For any two finite set A and B, we have the following rules.

1. n(A)         = n(A-B) + n(A∩B)
2. n(B)            =  n(B-A)  +  n(A∩B)
3. n(A∪B)       =  n(A-B)  +  n(A∩B)  +  n(B-A)
4. n(A∪B)       =  n(A)   +   n(B)  -  n(A∩B)
5. n((A∪B)      =  n(A)   +   n(B), when A∩B =
6. n(A) + n(A') =  n(U)

The following problems are bases on the above rules.

2.    If A and B are two sets such that A has 50 elements, B has 65 elements and AB has 100 elements, how many elements in A∩B?

3.     If A and B are two sets containing 13 and 16 elements respectively, then find the minimum and maximum number of elements in AB?

4.     If n( A∩B) = 5, n(AB) = 35, n(A) = 13, find n(B)?

5.     If n(A) = 26, n(B) = 10, n(A∪B) = 30, n(A') =17, find n(A∩B) and n(U)?

6.    If n(U) = 38, n(A) = 16,  n(A∩B) = 12, n(B') = 20, find n(A∪B)?

7.   Let A and B be two finite sets such that n(A-B) = 30, n(A∪B) = 180, n(A∩B)= 60, find n(B)?

8.    The population of a town is 10000. Out of these 5400 persons read newspaper A and 4700 read newspaper B. 1500 read both the newspapers. Find the number of persons who do not read either of the two papers.

9.    In a school, all the students play either foot ball or volley ball or both. 300 students play foot ball, 270 play volley ball and 120 students play both the games. Find

(i)  The number of students who play foot ball only?

(ii) The number of students who play volley ball only?

(iii)The total number of students in the school?

Students can try to solve the problems in this page 'Problems on set-VI' 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.