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

by Patricia

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)

 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