SOLUTION: Logic: Set and operations - Cardinal numbers and surveys A student conducted a survey at her school to find out the top goals students currently have. Let W = the set of those

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Question 1164083: Logic: Set and operations - Cardinal numbers and surveys
A student conducted a survey at her school to find out the top goals
students currently have. Let W = the set of those who want to get rich,
F = the set of those who want to start a family, and E = the set of those
who want to become experts in their fields. The student's findings were:
n (W) = 160; n (F) = 140; n (E) = 130; n (W∩F) = 95; n (E∩F) = 90;
n (W∩F∩E) = 80; n (E ') = 95; n [(W∪F∪E)'] = 10. Find the total number of
students interviewed.
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Find the total number of students interviewed.

THIS IS A TRICK QUESTION!

It's a givaway!  You're given n(E)=130 and n(E')=95, so
the total number of students = their sum = 225.

[All the other given information is not needed.]

Edwin
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

The total number of students in the school is  n(E) + n(E') = 130 + 95 = 225.


The number of those who was not interviewed is n([(W U F U E)']) = 10  (given).


Hence, the number of those who WAS interviewed is the COMPLEMENT  225 - 10 = 215.    


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All the rest info in the post is excessive, non-necessary and irrelevant.

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