# Set Theory

The concept of the “set” is one of the basic concepts of mathematics. In spite of this fact, there is no definition agreed on by the authority. Some mathematicians define sets as “the class of objects that have certain properties”. Although this definition is widespread, there are deficiencies.

Objects that form the set are called “elements”. The sets are represented with capital letters such as $A$, $B$, $C$, $X$, $Y$, and the elements of sets are represented with lower-case letter such as $a$, $b$, $c$, $x$, $y$. If $a$ is an element of $A$, this case is denoted by $a\in A$, if $a$ is not an element of $A$, this case is denoted by $a\notin A$. There are three types of representations to display the sets:

1. List method: In this representation, the elements of set are written into the curly braces, by putting the commas between the elements. In a set, an element cannot be written twice. As an example, $A=\{a,b,c,d,e\}$ can be given.

2. Venn diagram: In this representation, the elements of set are written inside a circle or rectangle. Let’s show the above example, $A=\{a,b,c,d,e\}$, by using Venn diagram: