Symbol name Symbol 
Meaning 
Example 
Set  {} 
A collection of objects 
X= {1,2,3} Y = {a, b, c, d} 
Not in  ∉ 
Elements in not in set 
X = {1,2,3,4} 5 ∉ X 
Belongs to ∈ 
Element is in the set 
X = {1,2,3,4} 4 ∈ X 
Empty set $\phi$ 
A set not having any elements 
A= {} or $A =\phi$ 
Equal set = 
Two set are equal when they have same elements 
X= {1,2,3} Y = {3,2,1} X=Y 
Subset  ⊆ 
A is said to be a subset of a set B if every element of A is also an element of B. 
A= {1,2,3} B= {3,2,1} A ⊆ B 
Proper Subset ⊂ 
A is said to be a proper subset of a set B if every element of A is also an element of B and A is not equal to B 
A= {1,2,3} B= {3,2,1,0} A ⊂ B 
Not Subset ⊄ 
A is not subset of B 
A= {1,2,3,4} B= {3,2,1,0} A ⊄ B 
Super set  ⊇ 
A is said to be a super set of a set B if every element of B is also an element of A 
A= {1,2,3,0} B= {3,2,1} A ⊇ B 
Proper Super set ⊃ 
A is said to be a super set of a set B if every element of B is also an element of A and A has more elements than B 
A= {1,2,3,0} B= {3,2,1} A ⊃ B 
Universal Set  U 
A Universal is the set of all elements under consideration, denoted by capital U. 

Union  ∪ 
Union of sets. 
A= {1,2,3,0} B= {3,2,1} A ∪ B = {0,1,2,3} 
Intersection ∩ 
Intersection of sets 
A= {1,2,3,0} B= {3,2,1} A ∩ B = {1,2,3} 
Complement  A^{c} 
Complement of set 
U = {1,2,3,4,5,6} A= {1,2,3} A^{c} = {4,5,6} 
Difference   
Difference of set. A B means elements present in A but not in B 
A= {1,2,3,0} B= {3,2,1} A – B = {0} 
Symmetric difference D 
The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A ? B Objects that belong to A or B but not to their intersection 
A= {1,2,3,0} B= {3,2,1} A D B = {0} 
Cartesian Product  X 
set of all ordered pairs from A and B A X B 
P= {1,2} Q= {5,4,2} P×Q= {(1,5), (1,4), (1,2), (2,5), (2,4), (2,2)} 
N 
the set of allnatural numbers 

Z 
the set of all integers 

Q 
the set of all rational numbers 

R 
the set of real numbers 

Z+ 
the set of positive integers 

Q+ 
the set of positive rational numbers 

Power set  P(A ) 
The collection of all subsets of a set X is called the power set of X 
A= {0,1} P(A) = { {}, {0}, {1}, {1,0} } 
Number of elements  n(A) 
Counts of number of elements in the set 
A= {0,1} n(A) =2 