|
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 | Ac |
Complement of set |
U = {1,2,3,4,5,6} A= {1,2,3} Ac = {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 all-natural 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 |
