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Set theory symbols





Set theory symbols

Set is a important mathematical tool .It has many symbols. Here I am giving list of all the Set theory symbols, meaning with examples
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

Quiz Time

Question 1 Two sets are given $A = {x : x - 11 = 0 }$ and $B = {x : x \; is \; an \; integral \; positive \; root \; of \;the \; equation x^2 - 12x -11 = 0}$.
A) $A \neq B $
B) $A = B $
C) $B \subset A $
D) $B= \phi$
Question 2 which of these is false ?
A) $N \subset Z$
B) $Q \subset R$
C) $N \subset R+$
D) None of the above
Question 3 which of these is a empty set
A) ${x|x^2 -9x +14=0 ,x \in R }$
B) ${x|x^2+1=0 ,x \in R }$
C) ${x|4x^2 -1=0 ,x \in R }$
D) ${x|x^2 -1=0 ,x \in R }$
Question 4 A = { 1,2,3,4,5} and B ={2,3,4,5,6,7} then A ∪ B
A) {1,6,7}
B) {1,2,3,4,5}
C) {2,3,4,5,6,7}
D) {1,2,3,4,5,6,7}
Question 5 A = { 1,2,3,4,5} and B ={1,2,3,4,5,6,7} then
A) $ B \subset A$
B) $ A \subset B$
C)$ A = B $
D)none of the above
Question 6A ={ 2,3,4} and B ={1,3,7},then A -B is
A. {2,4}
B. {2,4,3,7}
C. {3,7}
D. {1,7}


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