Suppose that among a group of sick people 10 have a headache (h), 10 have a...

Suppose that among a group of sick people
10 have a headache (h),
10 have a stomach ache (s), and
10 have a fever (f).
If
4 have (h) and (s),
4 have (s) and (f),
4 have (h) and (f), and
1 person has all three symptoms,
then there were 19 people in this group who had at least one of the three symptoms.

True or False?

Solutions

Expert Solution

True, There were 19 people in this group who had at least one of the three symptoms.

Explanations.

Let H be the set of all people having headache. Given number of people belongs to set H is 10, n(H)=10

Let S be the set of all people having stomach ache. Given number of people belongs to set S is 10, n(S)=10

Let F be the set of all people having fever . Given number of people belongs to set F is 10, n(F)=10

Also given

number of people belonging to sets H and S=4,

number of people belonging to sets S and F=4,

number of people belonging to sets H and F=4,

Finally 1 person has all three symptoms, means

Then is the group of all people having atleast one of the three symptoms.

Then number of people in the group having at least of the symptoms is

orchestra answered 1 year ago

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