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### Sets and Elements

```Date: 03/29/2003 at 14:02:57
From: Nanda
Subject: Set

Find the elements of the Set A={{1,2,3},{4,5},{6,7,8}} and determine
whether each of following is true or false:

a) 1EA
b} {1,2,3}CA
c) {6,7,8}EA
d) {{4,5}}CA
e) empty EA
f) empty CA

I believe that 1,2,3,4,5,6,7,8 are elements of set A. {1,2,3},{4,5},
{6,7,8} are subsets of set A and also elements of set A.
```

```
Date: 04/01/2003 at 16:53:37
From: Doctor Peterson
Subject: Re: Set

Hi, Nanda.

I assume you are using "E" to mean "is an element of" and "C" to
mean "is a subset of."

You have to take the definition of A literally. It does not say that
1, 2, 3, and so on are elements of the set; if they were, you would
be told

A = {1,2,3,4,5,6,7,8}

Rather, you are told that the elements of A are the SETS {1,2,3},
{4,5}, and {6,7,8}. A set is not its elements. And a subset is a SET
of elements, not an element itself.

So, for example, 1 is not an element of A, but {1,2,3} is, and {1,2,3}
is not a subset of A, but {{1,2,3}} is, since the latter is the subset
whose only element is the set {1,2,3}, which is in A.

I know it sounds strange, and normal people don't talk this way; but
math is all about precision - that's why it's written in symbols and
carefully defined words, rather than in ordinary English. Set
notation was invented to clarify this sort of thing, so that you can
say EXACTLY what you mean. That allows us to talk about sets of sets
without being entirely incomprehensible.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Logic

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