A universal set is a set that contains everything. We note the universal set with the letter
A Venn diagram is used to visualize the possible relations among a collection of sets.
U is called the universal set and it contains everything.
Complement of a set
The complement of a set A, Ā, contains all the elements in the universal set U but not in A.
The union of a set A and its corresponding complement is always equal to the universal set.
Venn diagram for Ā
The area in red represents the complement of A, Ā.
Venn diagram of A ∪ B
The red area represents the union of A and B.
Venn diagram of A ∩ B
The red area represents the intersection of A and B.
Venn Diagram for A – B
The red area represents the set difference between A and B.
Venn Diagram A ⊕ B
The red area represents the symmetric difference between A and B.
The symmetric difference between A and B is equals to the union of A and B less than the intersection of A and B.