Question

the results of a survey of common allergies was organized into a venn diagram.
answer the questions about the following sets:
d = {x | x is a person allergic to dogs}; c = {x | x is a person allergic to cats}; p = {x | x is a person allergic to pollen}
how many people are not allergic to any of the three choices?
how many people are allergic to all three choices?
how many people are allergic to both dogs and cats but not allergic to pollen?
how many people are allergic to cats only?

Explanation:

Step1: Find people not allergic to any

The number outside all circles in Venn diagram.
It is \(22\).

Step2: Find people allergic to all three

The intersection of all three sets \(D\), \(C\), \(P\).
It is \(1\).

Step3: Find people allergic to dogs and cats but not pollen

The intersection of \(D\) and \(C\) excluding \(P\).
It is \(7\).

Step4: Find people allergic to cats only

The part of \(C\) not overlapping with \(D\) or \(P\).
It is \(18\).

Answer:

Not allergic: \(22\)
Allergic to all three: \(1\)
Allergic to dogs and cats but not pollen: \(7\)
Allergic to cats only: \(18\)