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# A class has 175 students. The following table shows the number of students studying one or more of the following subjects in this class :SubjectNumber of studentsMathematics100Physics70Chemistry46Mathematics and Physics30Mathematics and Chemistry28Physics and Chemistry23Mathematics, Physics and Chemistry18How many students are enrolled in Mathematics alone, Physics alone and Chemistry alone ? Are there students who have not offered any of these three subjects ?

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Solution

## Ans 60M, 35P, 13C, 22 None.Here n(U)=175, n(M)=100, n(P)=70n(C)=46n(M∩P)=30, n(M∩C)=28n(P∩C)=28and n(M∩P∩C)=18To find n(M∩P′∩C′), n(P∩M′∩C′)n(C∩M′∩P′)and n(P′∩M′∩C′)Now similarly n(P′∩M′∩C′)=n(P)−n(P∩M)−n(P∩C)+n(P∩M∩C)}=70−30−23+18=35n(C∩M′∩P′)=n(C)−n(C∩M)−n(C∩P)+n(C∩M∩P)}=46−28−23+18=13and n(M′∩P′∩C′)=n(M∪P∪C)′¯z2−¯z1=(¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z2−z1)=n(U)−{S1∩S2∩S3}=n(U)−{n(M)+n(P)+n(C)−[(M∩P)−n(P∩C)−(M∩C)+n(M∩P∩C)}=175−100+70+46−30−23−28+18175−216−81+18=22  Suggest Corrections  0      Similar questions  Related Videos     