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Unions and Intersections


Date: 9 Feb 1995 15:30:17 -0500
From: Priscilla Warren NWISD
Subject: algebra

HELP!!!
I need to get help in Algebra.  My question is about intersections and 
unions.  In my text, there are these upside-down horseshoe looking things 
and there is no explanation of what they are or why they exist.  If you 
could explain them to me it would be very helpful.  And if you have any 
hints for passing Algebra, that would be great too.

                                  examples:
 
                  (A U B) U C     ( something like that)
                   A={x l x >-1}   ( a l represents a straight line)

                                    Thank you
           me now  :(
           me after you bail me out  :-}

                                 Paula e-mail: pfw@tenet.edu


Date: 9 Feb 1995 15:55:53 -0500
From: Dr. Sydney
Subject: Re: algebra

Dear Paula:

Hello!  We are glad you wrote Dr. Math with your questions!  

Before we talk about what unions and intersections are, let's look at the 
context in which we use unions and intersections.  We usually use them 
when talking about SETS.  A set is really just a collection of objects,
numbers, or whatever.  For instance, the natural numbers are a set.  Or, A 
in your example is a set. 

If we have two sets, A and B, then the union of A and B is notated:  A U B.  
A U B is a new set whose elements are the elements of both A and B.  So, 
if something is an element of either A or B, it is also an element of A U B.  
Suppose we have the sets:  A = {real numbers xlx>0} (so, this is just the 
positive real numbers) and B = {yl y is an integer}.  Then, A U B would be 
the set of positive real numbers and negative integers (0 is included).  

Now, the INTERSECTION of A and B is a little different.  The usual
notation for intersection is kind of an upside down U.  If you take the
union sign and flip it, you will get the intersection sign.  But, since
there is no such sign on the keyboard, I will use "i" to signify
intersection.  So A i B is a new set whose elements are in both A and B.
So, in the example above, A i B would be the set of all positive real
integers since positive real integers are in A (they are positive real
numbers) and they are also in B (they are integers).  Sometimes two sets
have no elements in common.  Then the intersection of the two sets is called
the empty set, often denoted {}.  For instance, if C = {1, 3, 5, ...} and D =
{2, 4, 6, ...}, then C i D = {}.

Let me just give one more example on a more finite level that might
make things clearer.  Suppose you have the following two sets:

K={0,1,2,3,6,8}
F={-1, 2, 3, 7/2, 8}

Then K U F is the set of all numbers that are in either K or F.  

So, K U F = {0,1,2,3,6,8,-1,7/2}

K i F is the set of all numbers that are in both K and F.  

So, K i F = {2,3,8} 

I hope this helps write back with any more questions you might have.  Good
luck with the algebra!

--Sydney, "dr. math"
    
Associated Topics:
High School Basic Algebra
High School Definitions
High School Sets

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