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A partition of a set A is by definition any collection of subsets of A such that they are not empty, that they have an empty intersection two by two and such that their union coincides with the whole set A.

We will say that two or more subsets of A form a partition of A if they satisfy three conditions:
1) nobody must be empty;
2) in any case two subsets are taken and their intersection must be empty;
3) their union must give us all the whole A.

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Set subtraction is a method which modifies a set by just removing the elements that belong to another set. This operation is represented by the symbols of minus or backslash (by - or \).
Ex: P\Q = P - Q = {x : x in P and x not in Q}
Q\P = Q - P = {x : x in Q and x not in P}

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the intersection of two sets: “A” and “B” is the set that contains all elements of A that also belong to B. we could write:
A ∩ B = { x| x( a ∈ A) ∧ ( b ∈ B)}

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                          STRICTLY INCLUDED

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                          STRICTLY INCLUDED

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The set B is strictly included in set A when every element of B is also element of A, but there are also elements of A that aren't elements of B.

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                           OPERATION ON SETS

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                           OPERATION ON SETS

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UNION
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
Elements can't be duplicated.
Ex:
A={1,3,6,8}
B={1,6,10,12}
A∪B={1,3,6,8,10,12}

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                               THE SUBSETS

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                               THE SUBSETS

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RELATION BETWEEN TWO SUBSETS
Some authors use the symbols ⊂ and ⊃ to indicate subset and superset respectively; that is, with the same meaning and instead of the symbols, ⊆ and ⊇.So for example, for these authors, it is true of every set A that A ⊂ A.
EXAMPLES:

The set A = {1, 2} is a proper subset of B = {1, 2, 3}, thus both expressions A ⊆ B and A ⊊ B are true.

The empty set { }, denoted by ∅, is also a subset of any given set X. It is also always a proper subset of any set except itself.

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                           UNIVERSAL SET

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                           UNIVERSAL SET

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The universal set is bigger than the others and contains them.
u=universal set.
{8,4,7} belongs to u.

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CAPITAL LETTER=SETS
SMALL LETTER=ELEMENTS
X=general element
A={a,e,i,o,u}=TABULAR FORM
A={x|x is a vocal of the alphabet}
|=such as

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BUILDER FORM
VENN'S DIAGRAM is a simple circle.In it,we can represent our set's elements.