Question

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 *

Answer 1

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,

$x = \frac{150}{15}$

:.x=10