NIMCET 2013 Question Paper with solutions

Question : 3 of 120

Marks: +1, -0

Find the number of elements in the union of 4 sets A. B. C and having 150,180,210 and 240 elements respectively, given that each pair of sets has 15 elements in common. Each triple of sets has 3 elements in common and
A ∩ B ∩ C ∩ D ≠ Φ

Validate

Solution:

As per the given condition,
A∪B∪C∪D=A+B+C+D–(A∩B)–(A∩C)+(A∩D)–(B∩C)–(B∩D)–(C∩D)
+(A∩B∩C)+(A∩B∩D)+(A∩C∩D)+(B∩C∩D)–(A∩B∩C∩D)

=150+180+210+240-15-15-15

-15-15-15+3+3+3+3-0

=780-90+15-3=795-90-3

=705-3=702

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