Overlapping Sets

Date: 02/10/98 at 22:37:58
From: Maneesh Puri
Subject: Sets

This question gave me a lot of problems due to its confusing English 
words:

We are given 87 tibbs. All 34 gibbs and 49 pibbs are tibbs. If exactly 
9 tibbs are gibbs and pibbs, then how many tibbs are neither pibbs nor 
gibbs?

Please help me out, it would be greatly appreciated...

Thank you.

Date: 02/11/98 at 04:32:32
From: Doctor Mitteldorf
Subject: Re: Sets

Dear Maneesh,

This problem is about overlapping sets. The words "tibbs" and "gibbs"
and "pibbs" are nonsense words made up for the problem and used 
because they are cute. We'll cal them T, G and P.

We are talking about Ts. Everything is a T. Think of T, G, and P as 
properties or attributes of these things, so things are allowed to be
more than one. Perhaps T means things and G means good and P means 
purple.

So we start with 87 things. They are all Things. 34 of them are Good
and 49 of them are Purple. But that doesn't make 84 all together, 
because there's some overlap. Some of them are both Good AND Purple.  
In fact, the next sentence tells you that the overlap is exactly 
9 things that are both Good and Purple. So we have 25 that are Good 
but not Purple, 40 that are Purple but not Good, and 9 that are both 
Good and Purple.  
   
The question is, how many does that account for? And, since we started 
with 87 Things all together, how many does that leave un-accounted
for? These are the Things that are neither Good nor Purple.

-Doctor Mitteldorf,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/