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:

1. How many people are not allergic to any of the three choices?

The number of people not in any of the three sets (D, C, P) is the number in the universal set outside all circles, which is given as 22.

The region common to all three circles (D, C, P) has the number 1, so that's the number of people allergic to all three.

The region for both dogs (D) and cats (C) but not pollen (P) is the part of the intersection of D and C that doesn't include P. From the Venn diagram, that number is 7.

Answer:

22

2. How many people are allergic to all three choices?