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Intersection of Sets: Physic(P) Chemistry(C) and Biology(B)

by Patricia
(Trinidad and Tobago)











































Solve the following problem using set theory.

If 100 students wrote exams, Physic(P) Chemistry(C) and Biology(B)

then,

n(PnCnB)=8
n(BuC)=76
n(BnC)=37
n(PuC)=28

How many students wrote Biology?

Comments for Intersection of Sets: Physic(P) Chemistry(C) and Biology(B)

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Jul 15, 2012
Intersection of Sets Physic(P) Chemistry(C) and Biology(B)
by: Staff


Answer:


If 100 students wrote exams, Physic(P) Chemistry(C) and Biology(B)

then,

n(P∩C∩B)=8
n(B∪C)=76
n(B∩C)=37
n(P∪C)=28

How many students wrote Biology?

I think there is some information missing from the problem statement.

Since n(B∩C) = 37 (the intersection of B & C = 37), both set B and set C must each be at least 37.

Since n(B∪C) = 76 (the union of set B and set C = 76), there are only three possibilities for set B and set C:

Set B = 37, 38, or 39
Set C = 39, 38, or 37

If n(P∪C) = 28 (the union of set P & C = 28), set P would have a negative value (which is impossible). Set C is at least 37, so n(P∪C) must be 37 or greater. n(P∪C) cannot be 28.

If you have additional information which applies to this problem, please submit it as a comment.





Thanks for writing.

Staff
www.solving-math-problems.com



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