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### Sets: Unions and Intersections

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Date: 12/17/97 at 19:04:03
From: Alison Lawless
Subject: Unions and Intersections

I want to know about complements, union, intersection, and sets of
would appreciate it very much.  Thank you so much!

Alison and her mother
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Date: 12/22/97 at 19:20:36
From: Doctor Barney
Subject: Re: Unions and Intersections

Here are a few examples.

A set is a group of elements that have some characteristic in common.
For example, let our set be all of the whole numbers from 1 to 20
inclusive. What do these elements have in common? They are all between
0.5 and 20.5, among other things.

A subset is a portion of the elements within a set that have some
additional characteristic in common. For example, let's define subset
A to be all of the numbers in my original set that are even, and
subset B numbers in the original set that are divisible by three.

Now, the INTERSECTION these two subsets A and B is the set of all
numbers that are in BOTH of these sets, just as a traffic intersection
is that part of the ground that is in two streets. In our example, the
intersection of A and B would be 6, 12, and 18, since these are the
only whole numbers between 1 and 20 that are both even and divisible
by 3.

The UNION of these two subsets is the set containing all elements that
are in BOTH A and B: in our example, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15,
16, 18, and 20. (Note that all elements contained in the intersection
of two sets are also contained in the union.)

The COMPLEMENT of a set is everything that is not in the set -
everything that would be needed to "complete" the area being
considered (in our case, the numbers 1 to 20.) For example, for the
sets I have defined above, the complement of A is all the odd numbers
between 1 and 20 inclusive, and the complement of B is  1, 2, 4, 5, 7,
8, 10, 11, 13, 14, 16, 17, 19, 20.

Here's an exercise. Remember that sets do not have to be numbers, they
can be lots of things. Let's use the capital letters A through Z.

Let A be the set of capital letters that have straight lines in them.

Let B be the set of capital letters that have curved parts.

1) List set A.

2) List set B.

3) List the complement of A.

4) List the complement of B.

5) What is the union of A and B?

6) List the letters in the intersection of A and B.

7) What letters are in the complement of the intersection of A and B?
Describe in words what makes these letters different from all the
others.

1) A,B,D,E,F,G,H,I,J,K,L,M,N,P,Q,R,T,U,V,W,X,Y,Z

2) B,C,D,G,J,O,P,Q,R,S,U

3) C,O,S

4) A,E,F,H,I,K,L,M,N,T,V,W,X,Y,Z

5) the whole alphabet

6) B,D,G,J,P,Q,R,U

7) A,C,E,F,H,I,K,L,M,N,O,S,T,V,W,X,Y,Z

None of these letters has both curved and straight lines in it.

-Doctor Barney,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Sets

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