# Thread: Sets - Assignment Question

1. ## Sets - Assignment Question

Hello, everyone! This is my first post here and some help would be greatly appreciated.

My question is about sets, here is the question I'm working on...

4. A Human Resource Department requested the following information concerning the 1605 employees; the number who are married; the number who are over 40 years of age, and the number who have passed the required physical examination. The data follows: (5 Marks)
715 are married
894 are over 40
911 have passed the physical
352 are married and over 40
365 are married and have passed the physical
320 are over 40 and have passed the physical
209 have passed the physical are married, and are over 40
Show that this information is in error. Illustrate with a Venn Diagram. (Show your work)

What I have so far is...

E = {e: e is an employee at the department}
O = {o: o is an employee who is over 40}
P = {p: p is an employee who has passed the physical}
M = {m:m is an employee who is married}

I have no idea where to go from here, any help would be great.

Thanks!

2. Sorry that I abandon your notation... Anyhow, let

A: Those who are married
B: Those over 40
C: Those who passed physical examination

Now A does not just hold employees that are just married but also some of those over 40 and those who passed the physical exam. This must be the case since A+B+C > 1605...the total number of employees.

Now draw a venn-diagram of the situation. That is draw three circles A, B and C that all overlap each other slightly.

"gibberish here before..."

Now let's comute the union

$\displaystyle A+B+C$

we will count each of the 2-way intersections $\displaystyle A\cap B,A\cap C$ and $\displaystyle B\cap C$ twice...so we have to subtract each of those once...

$\displaystyle A+B+C-(A\cap B+A\cap C+B\cap C)$

...but when we made this subtraction we also took away the 3-way intersection $\displaystyle A\cap B\cap C$ three times. As this intersection is counted three times in A+B+C we're now back to zero, hence we must add it once...

$\displaystyle A\cup B\cup C = A+B+C-(A\cap B+A\cap C+B\cap C)+A\cap B\cap C$

You have all the data for theese intersections and this might help you on the way...

3. Thanks a lot F.A.P, that helps greatly.