# 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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