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
 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}
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
P= {1,2}
Q= {5,4,2}
P×Q= {(1,5), (1,4),
(1,2), (2,5), (2,4), (2,2)}
the set of all-natural numbers
the set of all integers
the set of all rational numbers
the set of real numbers
the set of positive integers
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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