If n(AUBUC)=100, n(A)=4x,n(B)=6x,n(C)=5x, n(A∩B)=20,n(B∩C)=15, n(A∩C)=25 and n(A∩B∩C)=10, then the value of x is *
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Soln:
Given,
n(AUBUC)=100
n(A)=4x
n(B)=6x
n(C)=5x
n(A∩B)=20
n(B∩C)=15
n(A∩C)=25
n(A∩B∩C)=10
x=?
now,
using the formulae of cardinility of three sets based upon n(AUBUC),
n(AUBUC)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(A∩C)+n(A∩B∩C)
now,
Inserting all the values from given,
or,100=4x+6x+5x-20-15-25+10
or,100=15x-60+10
or,100=15x-50
or,100+50=15x
or,150=15x
or,
:.x=10
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