In order to illustrate the ideas involving universal sets, subsets and certain operations on sets in a clear and simple way, we make use of geometric figures. These figures are called Venn-Diagrams.
Usually universal set is denoted by rectangle and subsets are denoted by circles or ellipses.

Operations on Sets
Union of Sets
Let A and B be any two sets. The union of A and B is the set consisting of all the elements of A or B or both.
It is denoted as A∪B and read as 'A union B'.
A∪B={x: x∈A or x∈B}
Note that x∈A or x∈B also includes the possibility of x belonging to both A and B. If so, it should be taken as member of union set only once.
Properties of the Operation of Union
(i) A∪B = B∪A   (Commutative law)
(ii) (A∪B)∪C = A∪(B∪C)   (Associative law)
(iii) A∪Ï• = A   (Law of identity element, Ï• is the identity of ∪)
(iv) A∪A=A    (Idempotent law)
(v) U∪A=U  (Law of U)

Intersection of Sets 
The intersection of two sets A and B is the set consisting of all the common elements of A and B.
It is denoted by A∩B and read as 'A intersection B'.
A∩B={x: x∈A and x∈B}
Properties of the Operation of Intersection
(i) A∩B = B∩A   (Commutative law)
(ii) (A∩B)∩C = A∩(B∩C)   (Associative law)
(iii) A∩Ï• = Ï•   (Law of identity)
(iv) A∩A=A    (Idempotent law)
(v) U∩A=A  (Law of U)
(vi) A∩(B∪C)=(A∩B)∪(A∩C)  (Distributive law)
(vii) A∪(B∩C)=(A∪B)∩(A∪C) (Distributive law)
 

If A⊂B, then A∪B=B and A∩B=A
If A=Ï•, then A∪B=B and A∩B=Ï•

Difference of Sets
Let A and B be two sets, then their difference A-B is the set consisting of all elements of A which do not belong to B.
A-B={x: x∈A and x∉B}
Similarly, B-A={x: x∈B and x∉A}

Symmetric Difference of two sets
Let A and B be two sets. The symmetric difference of sets A and B is the set (A-B)∪(B-A) and is denoted by A∆B.
A∆B=(A-B)∪(B-A)={x: x∉(A∩B)}


Disjoint Set
Two sets A and B are said to be disjoint set if A∩B=Ï•, i.e. if they have no element in common.
If A∩B≠Ï•, then A and B are said to be intersecting or joint or overlapping sets.