Question 1164105: Logic: Set and operations - Cardinal numbers and surveys
A nurse conducted a survey with 75 patients admitted to the hospital.
Let B = (Blood) the set of patients with high Blood pressure,
C = (Cholesterol) the set of patients with high Cholesterol level,
S = (Smoke) the set of patients who Smoke cigarettes.
The information from the nurse is as follows:
n(B)=47; n(B∩S)=33; n(C)=46; n(B∩C)=31; n(S)=52; n(B∩C∩S)=21;
n[(B∩C)∪(B∩S)∪(C∩S)]=51.
Find the number of patients who
(a) had high blood pressure or high cholesterol, but not both?
(b) had fewer than two of the conditions listed?
(c) were smokers, but did not have high blood pressure or high cholesterol?
(d) did not present exactly two of the conditions on the list?
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
Begin with n(B∩C∩S)=g=21
Then go to n(B∩S)=f+g=33, and you can get f.
Then go to n(B∩C)=d+g=31, and you can get d.
Then go to n(B)=a+d+f+g=47, and you can get a.
Then go to n[(B∩C)∪(B∩S)∪(C∩S)]=d+g+f+h=51, and you can get h.
Then go to n(C)=d+e+g+h=46, and you can get e.
Then go to n(S)=f+g+h+i=52, and you can get i.
Finally, go to "75 patients", a+d+e+f+g+h+i+j=75, and you can get j.
(a) had high blood pressure or high cholesterol, but not both?
That's a+f+e+h.
(b) had fewer than two of the conditions listed?
That's a+e+i+j.
(c) were smokers, but did not have high blood pressure or high cholesterol?
That's i.
(d) did not present exactly two of the conditions on the list?
That's a+e+i+g+j
You can fill in the question marks in the Venn diagram, then add
them up to answer the questions.
Edwin
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