
 
Sets containing elements of various types,
e.g. red, green, blue ,


 
The empty set (the set containing no elements) 

 
The element belongs to the set ,
e.g. , red red, green, blue


 
The element does not belong to the set ,
e.g. , orange red, green, blue


 
The cardinality or the number of elements belonging to the set , e.g. , red, green, blue ,
.


 
The set is contained inside the set , thus all elements of are also elements of . In this situation we say that is a subset of .


 
The sets and contain the same elements,
e.g. a, b, cb, a, cc, b, a. The condition is true if and only if and . When does not contain the same elements as the notation is used.


 
The set is strictly contained inside the set , in other words it is true that but .


 
The set of elements satisfying the property ,
e.g. for it follows that and is even .


 
The power set of is the set of all subsets of , i.e. . For example if then .


 
The intersection of sets and , i.e. the set containing the elements that are found both in and . Thus and . For example . 

 
The intersection of sets , , ..., , i.e. the set containing the elements that are found in all of the given sets. In other words


 
The union of sets and , i.e. the set containing the elements that are found in either or . Thus or . For example . 

 
The union of sets , , ..., , i.e. the set containing the elements that are found in at least one of the given sets. In other words


 
The difference between and , i.e. the set containing the elements that are found in but are not found in . Thus and . For example . 

 
The Cartesian product of and , i.e. the set of all possible ordered pairs whose first component is an element of and whose second component is an element of . Thus and . For example . 