if n(AUBUC)=100, n(A)=4x, n(B)=6x, n(C)=5x, n(AUB)=20, n(BnC)=15, n(AnC)=25 and n(AnBnC)=10, then the value of x is_______.
Answers
Given : n(AUBUC)=100, n(A)=4x, n(B)=6x, n(C)=5x, n(AUB)=20, n(BnC)=15, n(AnC)=25 and n(AnBnC)=10
To Find : Value of x
Solution:
n(A∩B) = n(A) + n(B) - n(AUB)
=> n(AUB) = n(A) + n(B) - n(A∩B)
n(AUBUC) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
=> n(AUBUC) = n(A) + n(B) - n(A∩B) + n(C) - n(B∩C) - n(A∩C) + n(A∩B∩C)
=> n(AUBUC) = n(AUB) + n(C) - n(B∩C) - n(A∩C) + n(A∩B∩C)
=> 100 = 20 + 5x - 15 - 25 + 10
=> 100 = 5x - 10
=> 5x = 110
=> x = 22
value of x is 22
if n(A∩B)=20 then
n(AUBUC) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
100 = 4x + 6x + 5x - 20 - 15 - 25 + 10
=> 100 = 15x - 50
=> 150 = 15x
=> x = 10
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Answer:
answer is 22
Step-by-step explanation:
I hope may it helps you