Question relating to topic Sets

Question

In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100, Physics 70, Chemistry 40, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and chemistry 23, Mathematics, Physics and chemistry 18. How many students have offered Mathematics alone ?

Answer 1

Let

U = be the univesal set

M = be the number of students who take mathematics

P = be the number of  students who take physics

C = be the number of students who take chemisty

Given

n(U) = 175                                     n(M) = 100

n(P) = 70                                       n(C) = 40

n(MnP) = 30                                  n(MnC) = 28

n(PnC) = 23                                     n(MnPnC) = 18

required...........n(Mn(PuC)' )

from................ n(MnCnP' ) = n(MnC) - n(MnCnP) 

                                        = 28 -18 = 10

n(MnPnC' ) = n(MnP) - n(MnPnC)

                 =30 - 18 = 12

Therefore................................. n(Mn(PuC)' ) = n(MnCnP' ) + n(MnPnC' ) + n(MnPnC)

= 10 +12 +18  =40

40 students have offered Mathematics alone