Question

If n(A union B union C)= 100, n(A)=4x, n(B)=6x, n(C)=5x, n(A intersection B)=20, n(B intersection C)=15, n(A intersection C)=25 and n(A intersection B intersection C)=10, then the value of "x" is

Answer 1

Answer:

n(A∪B)=n(A)+n(B)−n(A∩B)−−−−−−−(1)

Given n(A)=7

n(B)=9

n(A∪B)=14

Substituting in 1

14=7+9−n(A∩B)

⇒n(A∩B)=16−14=2

Answer 2

Answer:

Hope this will be helpful....

Step-by-step explanation:   Solution;

n(AUBUC)= n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(A∩C)+n(A∩B∩C)

or, 100= 4x+6x+5x-20-15-25+10

or, 100= 15x-50

or, 100+50= 15x

or, 15x= 150

or, x= 150/15

∴ x= 10