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 ?

Question

Filo · Accepted Answer

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​ˉ​−z1​ˉ​=(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

Question Text	A class has $175$ students. The following table shows the number of students studying one or more of the following subjects in this class : How many students are enrolled in Mathematics alone, Physics alone and Chemistry alone ? Are there students who have not offered any of these three subjects ?
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

Practice questions from similar books

Subject	Number of students
Mathematics	$100$
Physics	$70$
Chemistry	$46$
Mathematics and Physics	$30$
Mathematics and Chemistry	$28$
Physics and Chemistry	$23$
Mathematics, Physics and Chemistry	$18$