Set theory was developed to explain about collections of objects, in Maths. Basically, the definition states it is a collection of elements. These elements could be numbers, alphabets, variables, etc. The notation and symbols for sets are based on the operations performed on them. You must have also heard of subset and superset, which are the counterpart of each other.
Sets have turned out to be an invaluable tool for defining some of the most complicated mathematical structures. TheyÂ are mostly used to define many reallife applications. Apart from this, there are also many types of sets, such as empty set, finite and infinite set, etc. These are explained widely with the help of Venn diagrams.
Sets in Maths
As we have already discussed, sets is a collection for different types of objects and collectively itself is called an object. For example, number 8, 10, 15, 24 are 4 distinct numbers, but when we put them together, they form a set of 4 elements, such that, {8, 10, 15, 24}.
In the same way, sets are defined in the Maths for a different pattern of numbers or elements. Such as, sets could be a collection of odd numbers, even numbers, natural numbers, whole numbers, real or complex numbers and all the set of numbers which comes in the number line.
Symbols Used For Representation of Sets
Let us see the different types of symbols we used while we learn about sets. Consider a Universal set (U) = {1, 2, 7, 9, 13, 15, 21, 23, 28, 30}
Symbol 
Symbol Name 
Meaning / definition 
Example 
{ }  set  a collection of elements  A = {1, 7, 9, 13, 15, 23},
B = {7, 13, 15, 21} 
A âˆª B  union  objects that belong to set A or set B  A âˆª B = {1, 7, 9, 13, 15, 21, 23} 
A âˆ© B  intersection  objects that belong to both the sets, A and B  A âˆ© B = {7, 13, 15 } 
A âŠ† B  subset  subset has few or all elements equal to the set  {7, 15} âŠ† {7, 13, 15, 21} 
A âŠ„ B  not subset  left set not a subset of right set  {1, 23} âŠ„ B 
A âŠ‚ B  proper subset / strict subset  subset has fewer elements than the set  {7, 13, 15} âŠ‚ {1, 7, 9, 13, 15, 23} 
A âŠƒ B  proper superset / strict superset  set A has more elements than set B  {1, 7, 9, 13, 15, 23} âŠƒ {7. 13. 15. } 
A âŠ‡ B  superset  set A has more elements or equal to the set B  {1, 7, 9, 13, 15, 23} âŠƒ {7. 13. 15. 21} 
Ã˜  empty set  Ã˜ = { }  C = {Ã˜} 
P (C)  power set  all subsets of C  C = {4,7},
P(C) = {{}, {4}, {7}, {4,7}} Given by 2^{s}, s is number of elements in set C 
A âŠ… B  not superset  set A is not a superset of set B  {1, 7, 9, 13, 15, 23} âŠ…{7, 13, 15, 21} 
A = B  equality  both sets have the same members  {7, 13,15} = {7, 13, 15} 
A \ B or AB  relative complement  objects that belong to A and not to B  {1, 9, 23} 
Ac  complement  all the objects that do not belong to set A  We know, U = {1, 2, 7, 9, 13, 15, 21, 23, 28, 30}
Ac = {2, 21, 28, 30} 
A âˆ† B  symmetric difference  objects that belong to A or B but not to their intersection  A âˆ† B = {1, 9, 21, 23} 
aâˆˆB  element of  set membership  B = {7, 13, 15, 21},
13 âˆˆ B 
(a,b)  ordered pair  collection of 2 elements  
xâˆ‰A  not element of  no set membership  A = {1, 7, 9, 13, 15, 23, 5 âˆ‰ A 
B, #B  cardinality  the number of elements of set B  B = {7, 13, 15, 21}, B=4 
AÃ—B  cartesian product  set of all ordered pairs from A and B  {3,5} Ã— {7,8} = {(3,7), (3,8), (5,7), (5, 8) } 
N_{1}  natural numbers / whole numbers Â set (without zero)  N_{1} = {1,2,3,4,5,â€¦}  6 âˆˆ N_{1} 
N_{0}  natural numbers / whole numbers Â set (with zero)  N_{0} = {0,1,2,3,4,â€¦}  0 âˆˆ N_{0} 
Q  rational numbers set  Q= {x  x=a/b, a,bâˆˆZ}  2/6 âˆˆ Q 
Z  integer numbers set  Z= {â€¦3,2,1,0,1,2,3,â€¦}  6 âˆˆ Z 
C  complex numbers set  C= {z  z=a+bi, âˆž<a<âˆž, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â âˆž<b<âˆž}  6+2iÂ âˆˆ C 
R  real numbers set  R= {x  âˆž < x <âˆž}  6.343434 âˆˆ R 
Related Links 

Operation On Sets Intersection Of Sets And Difference Of Two Sets 

Union And Intersection Of Sets Cardinal Number Practical Problems 
Download BYJU’SThe Learning App and learn the concepts of Maths with the help of personalised videos.