V. SET TYPES (continuation)

4. The Part set (or subset), namely the set whose members are part of another set member.
For example:
D = {0, 1, 2, 3, 4, 5, 6, 7} and
E = {3, 2, 6, 7}, it appears here that every element E is also a member of the set D.

It says H is "subset" of C and E ⊂ K be written.
"Subset" is denoted by ⊂.
Or say also set D "contains the set of" E and is written D ⊃ E. "Contains a set" is denoted by ⊃.
The set E is a subset of D if each member / element E is also a member of D. And because each member of E is contained in D, then E is said also contained in D.

How many subsets of a set?

From the set K = {2, 3, 5} we can form subsets: {}, {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5} and {2, 3, 5}.
Subsets obtained by 8 = 2³ (2 to the 3rd), 3 is the number of elements of K.

Thus the number of subsets of the set which has n element is 2ⁿ (two raised to the n th power).

Note: The empty set (null set) is a subset of all kinds of sets.
5. The Same set, namely two sets of all its members together.
For example:
If K = {a, b, c, d} and L = {b, d, a}, then is said to set K = set of L and is written K = L.
Note: The order of the members in each set not to be the same.

K and L is said to equal if every element of K is an element of L and vice versa

every element of L is an element of K as well.

6. The Universe set or the Universal set or Universum, namely a set that contains all objects that are being discussed.
The objects that being discussed had established a set of the Universe.
The Universe set is represented by "U" (from Universum / Universal). On the set of Venn diagrams, the Universe set depicted with rectangular.
Example:
             If A = {0, 2, 4, 6}, then set A is probably derived from
U = {integers}
U = {whole numbers}
U = {even numbers less than 8} or the set of another universe

containing 0, 2, 4, and 6.
Obviously when we talk about a set, of course this set is a subset of a specific universe set.