Set Notation

We can define the word square as “ a rectangle with all sides equal “, using the previously understood words “rectangle”, ”side”, and “ equal”. Such definitions are not always possible in mathematics, for example, how might we define the word point? The Greek geometry Euclid defined a point as “that which has no part”, a definition so meaningless and vague as to be unacceptable to the modern mathematician. Such words as “point” and “line” undefined basic words, which are used to define other words, but are not defined themselves. Set is also such undefined word. But sets are familiar; we speak of sets of furniture, collection of stamps, herd of cattle, classes of students, and so on.

A set, informally, is a collection of things. The "things" in the set are called the "elements", and are listed inside curly braces. For instance, if I were to list the elements of "the set of things on my bed when I wrote this lesson", the set would look like this:
{Pillow, blanket, a doll, guitar}
Sets are usually named using capital letters. This isn't a rule, as far as I know, but it does seem to be traditional. For example, let's name this set as "A". Then we have:
A = {pillow, blanket, a doll, guitar }
We use a special character to say that something is an element of a set. For instance, to say that "pillow is an element of the set A", we would write the following:

This is pronounced "pillow is an element of A".
The elements of a set can be listed out according to a rule, such as:
{x is a natural number, x < 10}
If you're going to be technical, you can use full "set-builder notation", which looks like this:

This is pronounced as "the set of all x, such that x is an element of the natural numbers and x is less than 10". The vertical bar is usually pronounced as "such that", and it comes between the name of the variable you're using to stand for the elements and the rule that tells you what those elements actually are. This same set, since the elements are few, can also be given by a listing of the elements, like this:

{1, 2, 3, 4, 5, 6, 7, 8, 9}
Listing the elements explicitly like this, instead of using a rule, is often called "using the roster method".
Your text may or may not get technical regarding the names of the types of numbers. If it does, these are the symbols to use:
N : the natural numbers
Z : the integers (bilangan bulat/utuh)
Q : the fractions
R : the real numbers

Disjointed Sets


Subsets
Sets can be related to each other. If one set is "inside" another set, it is called a "subset". Suppose A = {1, 2, 3} and B = {1, 2, 3, 4, 5, 6}. Then A is a subset of B, since everything in A is also in B. This is written as:

That sideways-U thing is the subset symbol, and is pronounced "is a subset of". To show something is not a subset, you draw a slash through the subset symbol, so the following:

...is pronounced as "B is not a subset of A".
For example :









If a set operation is required to produce a set which is either equal to another set or a subset of it, the condition is:



Intersections
If instead of taking everything from the two sets, you're only taking what is common to the two, this is called the "intersection" of the sets, and is indicated with an upside-down U-type character. An intersection operation between two sets produces a result which contains elements which are common to both sets:

These are pronounced as "set G intersect set H equals...", respectively.




Unions
If two sets are being combined, this is called the "union" of the sets, and is indicated by a large U-type character. A union operation between two sets produces a result which contains the members of both sets:

These are pronounced as "set K union set H equals …"

In the above example, the sets have a common element, the number five, but a union can be formed from disjointed sets.

EXERCISE
Say the following items in English, then write its technical method and say it in words as well.
A adalah himpunan bilangan cacah genap yang kurang dari 12’
B adalah himpunan bilangan cacah ganjil yang lebih dari 11dan kurang dari 20.
C adalah himpunan bilangan asli yang lebih dari atau sama dengan 5 dan kurang dari 7
D adalah himpunan bilangan cacah yang kurang dari atau sama dengan 4.
Jika Q= {x | 2 < x < 8, x∈ Bilangan bulat} dan R = himpunan factor dari 20, maka Q ∩ R adalah