*
Venn Diagrams and Applications *

** Course:
**For finite mathematics students
majoring in Business, Management, or Economics /Social & Life
sciences

Created by Kameswari Tekumalla for Synergy Project
(Feb 2002*)*

Uses websites about Venn diagrams produced by A.J.Ronald, Campbell, and NY State Exam Prep. Center.

** Background: **In the mid-nineteenth
century, John Venn (1834-1923), a Fellow of Cambridge University, devised
a scheme for visualizing logical relationships. His single contribution to
the field of Mathematics made him immortal. That contribution is the Venn
diagram. Venn wrote

Question:

Using the data from a survey of critical care hospital patients, complete the Venn diagram and answer the questions below.

80 patients were surveyed with the following results;

40 patients had Diabetes (D)

30 Patients** had** Heart** Disease
(H)**

30 Patients had Cancer (C)

15 Patients had Diabetes and Heart Disease

14 Patients had Diabetes and Cancer

18 Patients had Heart Disease and Cancer

10 Patients had all three

a) How many patients had exactly two of the ailments? _________

*
b*) How many patients suffered from none
of the three ailments? ________

c) How many patients suffered from Diabetes only? ______

d) How many patients had at least two of the ailments? ______