Expert: Paul Klarreich - 3/19/2009

Question
Hi,
I have to write an application problem using a Venn diagram
with three different sets and describe what
n(A'intersectedBintersectedC) results in for the
application.

Secondly, using the Cartesian product and the
multiplication principle, I have to describe what AxBxC,
the cartesian product for three sets A, B, C would look
like. How do I give an example of finding the product to
demonstrate the idea? How do I give a formula for counting
the number of elements in the set AxBxC? How could I prove
it's correct?

I've been stressing over these problems for a few days now.
I've tried a few different ways but everything comes out
wrong. Thank you for your time,
Lu

Answer
Questioner:   Lu
Country:  United States
Category:  Advanced Math
Private:  No
 
Subject:  Fundamentals of Modern Math makes me cry..
Question:  Hi,
I have to write an application problem using a Venn diagram
with three different sets and describe what
n(A'intersectedBintersectedC) results in for the
application.

Secondly, using the Cartesian product and the
multiplication principle, I have to describe what AxBxC,
the cartesian product for three sets A, B, C would look
like. How do I give an example of finding the product to
demonstrate the idea? How do I give a formula for counting
the number of elements in the set AxBxC? How could I prove
it's correct?

I've been stressing over these problems for a few days now.
I've tried a few different ways but everything comes out
wrong. Thank you for your time,
Lu

................................................  

A x B x C is defined as:

{ (a,b,c), where a is in A, b is in B, and c is in C.}

In other words, it's the set of ordered triples (we obsessive math types write 3-tuples) that we can make where we take:

The first  element from the first set.
The second element from the second set.
The third  element from the third set.

How many?  Use the fundamental counting principle (look that up in previous answers.) and get:

n(A x B x C) = n(a) n(b) n(c)

where n(a set) is its cardinality. (Look that up, too.)

As to your application program, I have no idea what you mean.