Question

In a school all the students play either football or volleyball or both .300 students play football .270 student play volleyball and 120 students play both games.1.the number of students who play football only2.the number of students who play volleyball only3.the total number of students in the school please say in detail [in set form]

Answer 1

Let the set of students who play football be denoted by 'F'
and the students playing volleyball be denoted by 'V'
and also the set which includes all the students be 'U'
Then the set which includes the students which play both football and volleyball is (FΠV) i.e intersection.
n(F)=300
n(V)=270
n(FΠV)=120
We know that,
n(U)=n(F)+n(V)-n(FΠV)
n(U)=300+270-120=450
Therefore total no.of students = 450
Then ,the set which includes the students which only play football is F-V
similarly,the set which includes the students which only plays volleyball is V-F.
We know that,
n(F-V)+n(FΠV)=n(F)
n(F-V)+120=300
n(F-V)=180
and,
n(V-F)+n(VΠF)=n(V)
n(V-F)+120=270 {VΠF=FΠV}
n(V-F)=150
Hence ,the total no.of students in school=450
,the total no.of students who only play football=180
,the total no.of students who only play volleyball=150.