Math, asked by purusothamanashwini, 8 months ago

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

Answered by amitnrw
7

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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Attachments:
Answered by kavithajoseph022
0

Answer:

answer is 22

Step-by-step explanation:

I hope may it helps you

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